CC BY 4.0 （除特别声明或转载文章外）
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Light bulbs
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#include <bits/stdc++.h>
#define maxm 1005
using namespace std;
pair<int, bool> pr[maxm << 1];
int t, n, m, l, r, cnt, x, y, b[maxm << 1];
int main(void)
{
scanf("%d", &t);
for (int i2 = 1; i2 <= t; i2++)
{
scanf("%d%d", &n, &m);
cnt = 0;
for (int i = 1; i <= m; i++)
scanf("%d%d", &x, &y), pr[++cnt] = {x, 1}, b[cnt] = x, pr[++cnt] = {y + 1, 0}, b[cnt] = y + 1;
sort(pr + 1, pr + 1 + cnt);
sort(b + 1, b + cnt + 1);
int len = unique(b + 1, b + cnt + 1) - b - 1;
// for(int i=1;i<=cnt;i++)cout<<pr[i].first<<" "<<pr[i].second<<endl;
// for(int i=1;i<=len;i++)cout<<b[i]<<endl;
int pt1 = 1, ans = 0, now = 0;
for (int i = 1; i <= len; i++)
{
ans += (now % 2) * (pr[pt1].first - pr[pt1 - 1].first);
while (b[i] == pr[pt1].first)
{
if (pr[pt1].second)
now++;
else
now--;
pt1++;
}
//-cout<<i<<" "<<b[i]<<" "<<pt1<<" "<<now<<" "<<ans<<endl;
}
printf("Case #%d: %d\n", i2, ans);
}
}
Counting Sequences I
喜闻乐见的打表题。
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#include <stdio.h>
int a[] = {0, 2, 1, 6, 12, 40, 30, 84, 224, 144, 135, 715, 627, 1326, 1274, 420, 480, 2720, 5202, 16530, 3800, 2590, 924, 16951, 552, 9300, 68575, 82134, 21168, 24360, 165300, 3720, 45632, 199584, 2244, 22015, 2520, 29304, 77330, 57798, 398320, 1285760, 4255062, 81270, 41624, 48510, 97290, 1479889, 106032, 11760, 180075, 132600, 3254004, 429936, 1267866, 38115, 2293060, 20948298, 40667106, 299425, 208860, 2325320, 344162, 7394058, 7636608, 82875520, 8580, 305118, 4013836, 171258, 173880, 11850965, 70320672, 1866318, 14396330, 4872900, 17100, 895356, 468468, 499122, 252800, 20509200, 7012845, 1391827, 578676, 25229190, 26418340, 211474989, 784847184, 497121123, 15339150, 49140, 393484, 1972158, 821748, 2924575, 53598240, 55872, 45638306, 15086610, 753390000, 50040450, 417498852, 18788230, 1649648, 1168440, 1202040, 63736369, 2461428, 68719050, 162308630, 564673856, 24864, 5916680, 12882, 83753235, 89751520, 869785371, 124424274, 827222264, 916501173, 142157979, 2679303, 3661464, 39416252, 40718500, 31500, 4096512, 135201152, 132178560, 5399940, 191928100, 764103895, 303683688, 755446880, 403450390, 878166801, 7620488, 63013698, 181404174, 188003060, 1490370, 40044, 7198477, 2965248, 73807320, 222581380, 897305600, 3241644, 486312756, 838638473, 668099857, 87240552, 277345965, 3652110, 279481895, 569777520, 909958004, 17438618, 102598248, 6080160, 331917600, 704201656, 12886128, 6522608, 11108130, 856576600, 6916639, 773139192, 393768648, 453484704, 5029110, 10088316, 597113652, 30102, 2755725, 479740800, 6824611, 490800468, 6727676, 453731610, 810770040, 174453052, 127995139, 76742980, 579462920, 6400260, 197469008, 621276832, 63131059, 3519180, 655161515, 315686842, 28570176, 246855106, 708291090, 7567560, 468395047, 15329358, 7998606, 803840600, 57548093, 624161197, 809432154, 689858065, 197982428, 630455180, 357065367, 320910720, 936082576, 87780, 963476640, 74767476, 379431305, 9754548, 380663735, 10031040, 156955682, 25639852, 20815512, 5347980, 198166963, 886901487, 225570529, 242056473, 501024386, 533868153, 603037815, 920524624, 245275990, 718210895, 212520, 12540528, 543375195, 461026027, 32361615, 540843679, 392427831, 168324999, 208713599, 700359503, 28225920, 380401421, 67909312, 81646278, 630637420, 1293931, 889031838, 949548624, 259817649, 549967486, 898626104, 686911972, 56583450, 24419560, 817851652, 16842240, 891525490, 17040642, 862442760, 43568980, 561311662, 17984466, 437032941, 809577120, 18959160, 388056851, 262408964, 560202110, 38713404, 657023276, 821728799, 818922105, 190585256, 635328541, 948130242, 157183696, 704797050, 309867908, 277830386, 51523419, 134870012, 749747645, 184738215, 448245518, 318027562, 275886879, 333883532, 395070958, 48524256, 475894014, 49114980, 236370917, 784569639, 979573108, 921821882, 773970379, 110038107, 105145128, 235499832, 26910000, 64267522, 208632348, 110356236, 214584532, 461333294, 560051640, 903997718, 590609103, 218012655, 780213045, 692419287, 439786580, 279209594, 383153779, 93074310, 814843017, 988535918, 205584668, 145543973, 54218796, 420841210, 489026136, 101531951, 476789328, 74482200, 664404815, 556029323, 35179968, 106293320, 217140, 72747180, 127035152, 215692694, 111253064, 388964221, 61191507, 848268878, 659514248, 487518216, 265388569, 771127213, 748161940, 681164077, 541338475, 70311036, 85182422, 882943718, 804827001, 59357303, 21376250, 43611750, 43737408, 807625711, 44111586, 713948361, 860057995, 984432333, 137008032, 883198273, 305220824, 581376307, 283279826, 758860975, 670467540, 619538990, 874650824, 656833322, 504482780, 851303417, 791600048, 321615528, 207289111, 969710687, 224897578, 969569932, 975009846, 12704182, 147213128, 181988425, 550724752, 138047730, 536076394, 19423120, 474768550, 534347422, 277774654, 873715625, 305094536, 448946783, 855709629, 60538530, 209522824, 693786590, 927479183, 18760111, 123571800, 467930686, 548061617, 339961478, 377197825, 929122116, 510292238, 260505648, 898560496, 606820688, 73823363, 167968493, 753754165, 643514715, 617757502, 468134774, 139190904, 429596203, 499872283, 804316856, 158784988, 500436898, 330820304, 833779290, 309908865, 798032191, 19144628, 330236216, 227597688, 791835097, 548987726, 78035958, 933622580, 464458901, 606535622, 336637759, 837971159, 466100351, 501035131, 722499131, 998404247, 40098260, 401772714, 106748090, 42495200, 86735880, 877149, 383556205, 196692, 263769300, 896584125, 250541410, 706926755, 322185268, 663522473, 595974710, 915622764, 342038221, 55675413, 585447394, 719165182, 809889789, 569918083, 97217522, 72682038, 663560186, 103370673, 909754905, 634643969, 791101815, 701424289, 688651692, 481800017, 873272360, 331481464, 944159323, 607048176, 450140201, 307580852, 633067279, 507471325, 680972531, 932698257, 847108034, 329935200, 841861733, 931230222, 86653572, 298186557, 317306433, 382511484, 941206421, 998651093, 269587042, 223414638, 901347339, 381257681, 299192826, 716507553, 865165128, 88498570, 843173027, 268662409, 919135809, 671588778, 222222296, 816798687, 794783532, 382042584, 329002916, 363573101, 606409032, 111669003, 820596994, 868832953, 599417016, 293953140, 806616576, 764889370, 63761101, 853583648, 276375792, 65522872, 998575523, 883199315, 676000997, 149580165, 348663191, 678678481, 255020512, 485229036, 109282577, 448477583, 149990544, 76877264, 304513527, 150568236, 655124776, 151988148, 534097455, 270093859, 221569978, 619992276, 544538574, 150812922, 389192157, 202124556, 637466796, 904314865, 928886810, 154958903, 986123802, 493231088, 174281319, 670239135, 620110933, 863183249, 934326167, 819168264, 7982499, 709372942, 504356707, 254984246, 388526852, 40220645, 796202131, 485121798, 860777029, 845478466, 228206320, 616806504, 373998577, 548461368, 270464656, 47395831, 356441469, 376758112, 144582797, 511930601, 460865219, 191102400, 759228371, 706166393, 656083619, 483915676, 233711788, 334721218, 366744996, 256254932, 939464893, 820630126, 744833546, 727795522, 280642674, 886252016, 350529523, 205557637, 252080132, 562214776, 526787415, 474826371, 467447759, 426265164, 903873639, 814861053, 652325400, 373440437, 687691947, 369572971, 323140786, 69302116, 43642259, 660284932, 778084009, 340284840, 31054896, 788787168, 688336753, 145029237, 985504152, 789054774, 962884714, 395571569, 233780504, 168115571, 494552394, 67447035, 202266088, 798703541, 395891121, 135046153, 403981400, 159247666, 143493859, 798227695, 55224865, 357009419, 454515132, 150274489, 178570260, 210983813, 498819674, 361042201, 426347031, 720670392, 170511627, 29604571, 941026002, 196725873, 117997015, 558944842, 993648602, 775173055, 482897329, 216451053, 588351508, 69968544, 839465698, 267745819, 497919246, 707866547, 515002033, 457109086, 791806544, 756143730, 501423063, 621969865, 65435703, 1760928, 294520520, 295850520, 171480964, 75037306, 746533086, 735283669, 993956457, 761593809, 576182646, 29796753, 307091250, 750194451, 127938676, 113624041, 684683623, 559264596, 910352698, 632570004, 922079143, 700674648, 107768085, 12803389, 315230643, 69719392, 684737497, 713196061, 500895558, 489199334, 118998513, 154225376, 601094140, 605921272, 635704768, 226235052, 487165332, 520733089, 660828412, 510296466, 70596855, 87989882, 814956472, 989764782, 509684340, 105100373, 56635131, 878945228, 75750103, 889601833, 805395626, 1018164, 550074525, 591104443, 507686325, 106832893, 121280127, 252901789, 754281360, 55124492, 539232854, 378979248, 37596279, 871423269, 46434673, 303502248, 831327476, 682341354, 984281639, 518822386, 209012379, 373818194, 280886837, 200784330, 835954781, 952391185, 708363654, 854813534, 31991942, 892048110, 573477097, 726697464, 481008185, 838200926, 184369893, 235370739, 451975003, 442549874, 346154363, 664956781, 751500417, 766800077, 612475552, 603329623, 900187875, 480110290, 124363866, 359437181, 75806737, 428987741, 280183261, 255034614, 138883350, 744685088, 284786294, 118056680, 857162814, 86710025, 111734528, 902382760, 671383828, 390551308, 330049507, 268637353, 432803347, 734228779, 52835114, 1215240, 794111495, 169789549, 974873498, 2455488, 7533512, 434190168, 275570612, 631324980, 694449373, 796264418, 520361981, 566911084, 141925319, 310049960, 259421112, 389584998, 465612970, 741650255, 15626799, 817985602, 955298916, 373067244, 749792253, 519072048, 709957667, 352435327, 307806691, 103532642, 931274568, 55054546, 508958223, 334183064, 784907041, 514706626, 765771029, 654170840, 327024525, 265119102, 997643052, 198350910, 662827123, 380189614, 818560301, 792090648, 648806412, 565603500, 370645480, 697510117, 191781902, 714187644, 68919578, 775673314, 802156026, 327313830, 981974078, 353487139, 356667790, 612781218, 123314900, 720381882, 234631072, 725805855, 662954402, 249842351, 851066342, 815392996, 425744774, 876287207, 974652300, 945822500, 514375749, 436698245, 389982090, 638765679, 953468095, 254442313, 374933677, 546717955, 718111373, 785286672, 40983236, 854513483, 869334736, 706111287, 760755468, 477779463, 106101468, 555653287, 467970542, 448928923, 244409126, 132202982, 45032659, 183576156, 723789448, 331709380, 646468723, 7618074, 634316500, 507395929, 739563824, 358168213, 307141879, 906239919, 383552291, 603072554, 927872338, 992793541, 106993994, 959368012, 239359520, 958645519, 97766556, 731202273, 524097717, 897101113, 696767626, 119789136, 506989682, 454761793, 260903034, 924524905, 436819382, 460758311, 350337118, 742856580, 632420149, 647647472, 119844310, 736127169, 625054057, 951065689, 523298143, 55071410, 495972022, 948411706, 661284847, 543872197, 327608264, 717372706, 816254369, 365398585, 849672317, 892787726, 91534997, 561260042, 200048155, 615104795, 893042933, 398432214, 686351665, 720195287, 512767529, 354028115, 730207706, 758504201, 989913501, 338764389, 727411977, 595038002, 181853274, 396483757, 432243270, 485643332, 877319158, 140454505, 745000975, 611498115, 395296858, 292419313, 191311267, 853411926, 446691238, 580623351, 397273986, 740302027, 954140674, 368525042, 496213255, 99729633, 819445721, 223561524, 791028285, 725818523, 391350585, 1864380, 471961435, 460468174, 110523007, 188242539, 601916944, 869058584, 154915878, 373400807, 566756325, 525860165, 283085347, 96330146, 735389956, 947087381, 931924086, 914515318, 998942683, 972426722, 825933663, 917666394, 34729893, 639560602, 6392083, 997565381, 357134307, 688692967, 810741123, 779912339, 146525680, 451628321, 76797290, 548922635, 837490667, 170994838, 423345877, 129090457, 818477932, 59887299, 921448552, 696661704, 376243808, 23624929, 593822289, 7631378, 669643487, 457636516, 966360400, 169535581, 221258907, 804640886, 946579310, 759818681, 502069767, 488732898, 189768562, 874303301, 139105262, 74788345, 342563828, 814987229, 518441160, 486616097, 264157861, 781755606, 220233735, 293262794, 47192702, 744589011, 502087245, 644009612, 698703472, 933094451, 437047482, 973869717, 353009606, 311989248, 891410657, 574727666, 112067918, 586375307, 881918259, 178185268, 777795697, 383723936, 833629481, 705150479, 74265245, 146538580, 8917416, 364089236, 603597984, 669065439, 56801053, 340987474, 491430879, 167637977, 795083390, 514321126, 628034835, 73435079, 331767, 587868050, 925257726, 296025157, 4583880, 94548187, 27129928, 687485123, 153476345, 971505419, 240975411, 655010663, 784968058, 730969296, 549515837, 190402315, 812520333, 837233823, 580225672, 214692760, 968382817, 349551304, 872030955, 913289980, 727860843, 904421703, 525699547, 718377743, 86469381, 290404560, 349078279, 893847202, 18047457, 532613704, 687247627, 2426604, 48290411, 565094863, 952919356, 929554956, 331258640, 442063720, 109848068, 546344621, 689175476, 639256606, 61256976, 666659774, 900152643, 609635265, 59764974, 747453865, 82276239, 608996864, 188466878, 754517941, 873055451, 767056914, 376133080, 452677803, 236489791, 894446733, 124367604, 798555100, 929966018, 218211120, 159167283, 832017848, 764662630, 12452848, 291468549, 310525484, 224341245, 461404668, 171786431, 424308103, 659875206, 914488331, 233375053, 88095382, 705038270, 127859679, 727692572, 845393508, 275751707, 924561422, 821163746, 823207036, 198946905, 361117238, 855245947, 882535045, 661613930, 922227576, 132563739, 700201660, 134187592, 378134320, 206304426, 647483758, 446869221, 537761316, 836501507, 737942573, 101462914, 254976945, 984195498, 820249000, 513006904, 883675686, 557168210, 450052408, 525873517, 546387405, 452391975, 919501853, 832568757, 15771841, 484526551, 175134775, 16034822, 211327375, 330263119, 617274503, 691022710, 7120151, 858681594, 335637869, 433252481, 458555250, 651254990, 663858506, 194778510, 921937639, 458334254, 851969973, 369221056, 832965539, 224982723, 278741460, 208135475, 527091615, 13727746, 933648460, 979217271, 977908109, 699347534, 605275061, 680006844, 138207385, 476420524, 454337834, 432857762, 329129493, 249917198, 635207838, 925775672, 319266038, 887064863, 955698465, 800487244, 890273204, 197837460, 772046625, 448568903, 994270983, 2202083, 337825364, 314855310, 571777590, 100930605, 804271258, 896561440, 209505045, 636202604, 654077994, 354744867, 654916048, 892346636, 900874886, 875082407, 820397405, 744408326, 319524142, 857109769, 825251278, 139189036, 740415394, 734723593, 549082845, 449981465, 682193071, 264849052, 548097428, 256591101, 904105174, 216886060, 546346517, 925358843, 354864453, 722718671, 321846273, 425509709, 550501155, 887998324, 242630205, 341203401, 567799310, 945919477, 234461536, 992565773, 532984267, 706692878, 477501163, 907735581, 385409880, 24084117, 152826686, 535828167, 505728432, 576019572, 637926206, 63597142, 486048180, 175547747, 204747271, 448146096, 457727918, 488912075, 108205956, 810889345, 741657960, 989265235, 90709325, 667608082, 363714689, 842189216, 938344764, 621625602, 73955312, 150044362, 114626882, 431495595, 507500775, 572205175, 382879956, 114216690, 806893429, 210570498, 455186137, 425417333, 386398714, 596827545, 263703787, 703382548, 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935059609, 76336473, 816549921, 272103268, 768416972, 859456661, 463819251, 32608561, 698776266, 688501880, 939605786, 5192087, 844383395, 550698387, 396220525, 25232358, 122324978, 874042807, 493690026, 447201459, 855822480, 585455069, 894491961, 989605241, 539114271, 273794598, 517458429, 753561258, 41854924, 936179443, 534463507, 784177424, 645763670, 839030396, 385673367, 619137125, 536106422, 960441507, 423636834, 736931653, 391970025, 553811901, 398314174, 528605644, 310709962};
int main()
{
int t, n;
for (scanf("%d", &t); t--;)
{
scanf("%d", &n);
printf("%d\n", a[n]);
}
}
Stone game
完全背包搞一搞，要滚动内存。
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct Mod
{
const ll M, SM;
Mod(ll M) : M(M), SM(sqrt(M) + 0.5) {}
ll qadd(ll &a, ll b) const { return a += b, a >= M ? a -= M : a; } //假如a和b都已经在同余系内，就不必取模了，取模运算耗时很高
ll add(ll a, ll b) const { return qadd(a = (a + b) % M, M); } //考虑a和b不在同余系内甚至为负数的情况
ll mul(ll a, ll b) const { return add(a * b, M); }
ll inv(ll a) const { return pow(a, M - 2); } //要求M为素数，否则return pow(a, phi(M) - 1);
ll pow(ll a, ll b) const
{
if (b < 0)
a = inv(a), b = -b;
ll r = 1;
for (a = add(a, M); b; b >>= 1, a = mul(a, a))
if (b & 1)
r = mul(r, a);
return r;
}
/*
ll mul(ll a, ll b) const { return add(a * b, -M * ll((long double)a / M * b)); }
ll mul(ll a, ll b) const //无循环快速计算同余乘法，根据a*b是否爆ll替换a*b%M，需要a<M且b<M，可以调用时手动取模
{
ll c = a / SM, d = b / SM;
a %= SM, b %= SM;
ll e = add(add(a * d, b * c), c * d / SM * (SM * SM - M));
return add(add(a * b, e % SM * SM), add(c * d % SM, e / SM) * (SM * SM - M));
}
ll inv(ll a) const
{ //模m下a的乘法逆元，不存在返回-1（m为素数时a不为0必有逆元）
ll x, y, d = gcd(a, M, x, y);
return d == 1 ? add(x, M) : -1;
}
vector<ll> sol(ll a, ll b) const //解同余方程，返回ax=b(mod M)循环节内所有解
{
vector<ll> ans;
ll x, y, d = gcd(a, M, x, y);
if (b % d)
return ans;
ans.push_back(mul((b / d) % (M / d), x));
for (ll i = 1; i < d; ++i)
ans.push_back(add(ans.back(), M / d));
return ans;
}
ll log(ll a, ll b) const
{
unordered_map<ll, ll> x;
for (ll i = 0, e = 1; i <= SM; ++i, e = mul(e, a))
if (!x.count(e))
x[e] = i;
for (ll i = 0, v = inv(pow(a, SM)); i <= SM; ++i, b = mul(b, v))
if (x.count(b))
return i * SM + x[b];
return -1;
}
*/
} M(1e9 + 7);
const ll N = 333;
ll a[N], f[N << 9], s[N << 9];
int main()
{
ll t, n;
for (scanf("%lld", &t); t--;)
{
scanf("%lld", &n);
ll sum = 0, ans = 0;
for (int i = 0; i < n; ++i)
scanf("%lld", &a[i]), sum += a[i];
sort(a, a + n, greater<ll>());
memset(s, 0, sizeof(s));
f[0] = s[0] = 1;
for (int i = 0; i < n; ++i)
for (int j = sum; j >= 0; --j)
{
M.qadd(s[j], f[j] = j >= a[i] ? s[j - a[i]] : 0);
if (j - a[i] <= sum - j && sum - j <= j)
M.qadd(ans, f[j]);
}
printf("%lld\n", ans);
}
}
Peekaboo
过的人略少，但其实很简单，圆上整点模板题。先求出两个圆$x^2+y^2=a$,$x^2+y^2=b$上所有整点，随后两两暴力检查距离是否为 c 即可。圆上整点是一个数论问题，网上题解一大把。
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
inline ll pf(ll x) { return x * x; }
#define ok(xa, ya, xb, yb) \
{ \
if (pf(c) == pf((xa) - (xb)) + pf((ya) - (yb))) \
ans.emplace_back(xa, ya, xb, yb); \
}
vector<ll> work(ll r)
{
vector<ll> d, ans;
for (ll i = 1; i * i <= r * 2; ++i)
if (r * 2 % i == 0)
d.push_back(i), d.push_back(r * 2 / i);
for (ll i = 0; i < d.size(); ++i)
{
for (ll rd2 = 2 * r / d[i], a = 1; 2 * a * a <= rd2; ++a)
{
ll A = a * a, B = rd2 - A, b = sqrt(B + 0.5);
if (b * b == B && A != B && __gcd(A, B) == 1)
{
ans.push_back(d[i] * a * b);
}
}
}
sort(ans.begin(), ans.end());
ans.resize(unique(ans.begin(), ans.end()) - ans.begin());
for (int n = ans.size(), i = 0; i < n; ++i)
ans.push_back(-ans[i]);
ans.push_back(0);
ans.push_back(r);
ans.push_back(-r);
return ans;
}
int main()
{
ll t, a, b, c;
for (scanf("%lld", &t); t--;)
{
scanf("%lld%lld%lld", &a, &b, &c);
vector<ll> xa = work(a), xb = work(b);
vector<tuple<ll, ll, ll, ll>> ans;
for (ll i = 0; i < xa.size(); ++i)
{
ll ya = sqrt(a * a - xa[i] * xa[i]);
for (ll j = 0; j < xb.size(); ++j)
{
ll yb = sqrt(b * b - xb[j] * xb[j]);
ok(xa[i], ya, xb[j], yb);
ok(xa[i], -ya, xb[j], yb);
ok(xa[i], ya, xb[j], -yb);
ok(xa[i], -ya, xb[j], -yb);
}
}
sort(ans.begin(), ans.end());
ans.resize(unique(ans.begin(), ans.end()) - ans.begin());
cout << ans.size() << '\n';
for (auto p : ans)
printf("%lld %lld %lld %lld\n", get<0>(p), get<1>(p), get<2>(p), get<3>(p));
}
}
Digit sum
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#include <bits/stdc++.h>
using namespace std;
const int maxn = 50;
int T, N, b;
int a[maxn], ad[maxn];
int main()
{
scanf("%d", &T);
for (int t = 1; t <= T; t++)
{
scanf("%d%d", &N, &b);
int d = 0;
a[d] = 1;
while (a[d] < N)
a[++d] = a[d - 1] * b;
int tot = b * (b - 1) / 2, ans = 0;
for (int i = 1; i <= d; i++)
ad[i] = tot * i * a[i - 1];
for (int i = d; i >= 0; i--)
{
int now = N / a[i];
N %= a[i];
ans += (now - 1) * now / 2 * a[i] + now * (N + 1);
ans += now * ad[i];
}
printf("Case #%d: %d\n", t, ans);
}
}