#pragma GCC optimize("O3") #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize("Ofast") #pragma GCC optimize("inline") #pragma GCC optimize("-fgcse") #pragma GCC optimize("-fgcse-lm") #pragma GCC optimize("-fipa-sra") #pragma GCC optimize("-ftree-pre") #pragma GCC optimize("-ftree-vrp") #pragma GCC optimize("-fpeephole2") #pragma GCC optimize("-ffast-math") #pragma GCC optimize("-fsched-spec") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("-falign-jumps") #pragma GCC optimize("-falign-loops") #pragma GCC optimize("-falign-labels") #pragma GCC optimize("-fdevirtualize") #pragma GCC optimize("-fcaller-saves") #pragma GCC optimize("-fcrossjumping") #pragma GCC optimize("-fthread-jumps") #pragma GCC optimize("-funroll-loops") #pragma GCC optimize("-freorder-blocks") #pragma GCC optimize("-fschedule-insns") #pragma GCC optimize("inline-functions") #pragma GCC optimize("-ftree-tail-merge") #pragma GCC optimize("-fschedule-insns2") #pragma GCC optimize("-fstrict-aliasing") #pragma GCC optimize("-falign-functions") #pragma GCC optimize("-fcse-follow-jumps") #pragma GCC optimize("-fsched-interblock") #pragma GCC optimize("-fpartial-inlining") #pragma GCC optimize("no-stack-protector") #pragma GCC optimize("-freorder-functions") #pragma GCC optimize("-findirect-inlining") #pragma GCC optimize("-fhoist-adjacent-loads") #pragma GCC optimize("-frerun-cse-after-loop") #pragma GCC optimize("inline-small-functions") #pragma GCC optimize("-finline-small-functions") #pragma GCC optimize("-ftree-switch-conversion") #pragma GCC optimize("-foptimize-sibling-calls") #pragma GCC optimize("-fexpensive-optimizations") #pragma GCC optimize("inline-functions-called-once") #pragma GCC optimize("-fdelete-null-pointer-checks") #pragma GCC optimize("Ofast") //#pragma GCC target("avx,avx2,fma") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") //#pragma GCC optimization ("unroll-loops") #include using namespace std; const long long int mod = 1e9 + 7; using lint = long long; lint ipow(lint x, lint p){ lint ret = 1, piv = x; while(p){ if(p & 1) ret = ret * piv % mod; piv = piv * piv % mod; p >>= 1; } return ret; } vector berlekamp_massey(vector x){ vector ls, cur; int lf, ld; for(int i=0; i c(i-lf-1); c.push_back(k); for(auto &j : ls) c.push_back(-j * k % mod); if(c.size() < cur.size()) c.resize(cur.size()); for(int j=0; j=(int)cur.size()){ tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod); } cur = c; } for(auto &i : cur) i = (i % mod + mod) % mod; return cur; } int get_nth(vector rec, vector dp, lint n){ int m = rec.size(); vector s(m), t(m); s[0] = 1; if(m != 1) t[1] = 1; else t[0] = rec[0]; auto mul = [&rec](vector v, vector w){ int m = v.size(); vector t(2 * m); for(int j=0; j= mod) t[j+k] -= mod; } } for(int j=2*m-1; j>=m; j--){ for(int k=1; k<=m; k++){ t[j-k] += 1ll * t[j] * rec[k-1] % mod; if(t[j-k] >= mod) t[j-k] -= mod; } } t.resize(m); return t; }; while(n){ if(n & 1) s = mul(s, t); t = mul(t, t); n >>= 1; } lint ret = 0; for(int i=0; i x, lint n){ if(n < x.size()) return x[n]; vector v = berlekamp_massey(x); if(v.empty()) return 0; return get_nth(v, x, n); } struct elem{int x, y, v;}; // A_(x, y) <- v, 0-based. no duplicate please.. vector get_min_poly(int n, vector M){ // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j} vector rnd1, rnd2; mt19937 rng(0x14004); auto randint = [&rng](int lb, int ub){ return uniform_int_distribution(lb, ub)(rng); }; for(int i=0; i gobs; for(int i=0; i<2*n+2; i++){ int tmp = 0; for(int j=0; j= mod) tmp -= mod; } gobs.push_back(tmp); vector nxt(n); for(auto &i : M){ nxt[i.x] += 1ll * i.v * rnd1[i.y] % mod; if(nxt[i.x] >= mod) nxt[i.x] -= mod; } rnd1 = nxt; } auto sol = berlekamp_massey(gobs); reverse(sol.begin(), sol.end()); return sol; } lint det(int n, vector M){ vector rnd; mt19937 rng(0x14004); auto randint = [&rng](int lb, int ub){ return uniform_int_distribution(lb, ub)(rng); }; for(int i=0; i v = {0,1,12,486,42720,6615000,599484313,291848814,940887432,359615350,678345397,322826110,535714982,742062744,275016949,548819915,964501078,794648746,828747937,69089868,741116640,75830509,727542734,812134260,286524125,676582511,902705458,963000930,895570778,48289307,436587873,371570836,78861901,393155986,146890024,155968224,760007060,802173869,564913985,544330500,593163214,614684977,41806771,184940152,354253130,688089745,415553708,506060624,838728450,347359094,880366393,38445594,145839250,532951651,339768096,705417752,752436057,722273969,707711155,291281728,678851651,306869667,528543445,608449438,637758609,511419998,189522127,539198238,976511058,137637644,567893827,712292474,483724407,144030241,352906962,286436655,415790448,889377652,708543672,698972882,2227249,375311698,12706004,319374486,445060133,858976976,903048927,381444308,28964427,200595163,378622939,430073785,776494743,569865690,324028448,30735347,818180383,29846318,171353031,306151317,349657766,203277272,257603204,445394158,961031134,835876250,453364929,40963429,900873690,676838279,750343392,60732353,808972607,418199935,611315700,201220971,595948166,3021017,219229404,310042865,837967183,799799714,908933542,360629668,178207868,938048519,359242276,267360807,775282082,303462357,21259614,830306424,957699545,617048678,567659329,915387921,516356820,941695836,441091405,825869132,249684244,541630976,680954659,715006344,780441213,945062457,311238792,275888330,869088070,13485483,554277149,528097697,289344106,242071659,343715588,894667025,435282364,861765961,545885648,219126178,443319492,810678130,87810324,295692167,677616530,520705385,958336952,538207320,102651757,921505468,987657682,899543047,554802955,260789336,147235238,518184547,458687170,834132193,85842407,132474347,18443298,20712898,776024629,318144571,135032292,169104531,338621454,568160907,773773637,611343724,941675529,421663599,46494321,352953009,859275842,28445453,795571755,277478322,36491572,308951601,42877477,45478378,835603395,911173515,779732381,460227823,704718755,890758157,263769275,24367956,56800872,759406886,707041024,441883162,847588722,407069185,964381663,991495584,978180546,823630043,472812875,46508032,908711620,114842792,241953541,899682386,468656526,704901940,860798688,285737460,694265118,600701486,761800699,983662100,210014373,853030700,479360400,836064310,222627469,288868756,148089720,629542596,651176402,505889923,277863369,874618228,235127684,56214717,150865256,900218392,525917753,98433561,89421797,9759576,3785752,890905346,408916885,571587478,1240723,788862015,684915086,452585634,683514363,42516154,504763805,702281540,519713335,662196321,535523230,625351283,198271669,461933891,281194101,87361923,657513132,737855012,86361732,177296649,798695354,538933444,859771287,862394526,733813024,158472875,468130323,619736582,759819904,468126957,903923107,515557302,881517997,201340780,597288151,572042172,176699155,598756729,28679134,925416910,221296507,726048467,826282086}; int main(void) { cin.tie(0); ios::sync_with_stdio(false); int n; cin >> n; cout << guess_nth_term(v,n) << '\n'; return 0; }