#include<bits/stdc++.h>#define mp make_pair#define rep(i,a,n) for (int i=a;i<n;i++)#define per(i,n) for (int i=n-1;i>=a;i--)#define pb push_back#define mp make_pair#define all(x) (x).begin(),(x).end()#define fi first#define se second#define SZ(x) ((int)(x).size())using namespace std;typedef vector<int> VI;typedef long long ll;typedef pair<int,int> PII;const ll mod = 1000000007;ll powmod(ll a,ll b) { ll res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1)res = res * a%mod; a = a * a%mod; }return res; }// headll n;namespace linear_seq { const int N = 10010; ll res[N],base[N],_c[N],_md[N]; vector<int> Md; voID mul(ll *a,ll *b,int k) { rep(i,0,k + k) _c[i] = 0; rep(i,k) if (a[i]) rep(j,0,k) _c[i + j] = (_c[i + j] + a[i] * b[j]) % mod; for (int i = k + k - 1; i >= k; i--) if (_c[i]) rep(j,SZ(Md)) _c[i - k + Md[j]] = (_c[i - k + Md[j]] - _c[i] * _md[Md[j]]) % mod; rep(i,k) a[i] = _c[i]; } int solve(ll n,VI a,VI b) { // a 系数 b 初值 b[n+1]=a[0]*b[n]+... // printf("%d\n",SZ(b)); ll ans = 0,pnt = 0; int k = SZ(a); assert(SZ(a) == SZ(b)); rep(i,k) _md[k - 1 - i] = -a[i]; _md[k] = 1; Md.clear(); rep(i,k) if (_md[i] != 0) Md.push_back(i); rep(i,k) res[i] = base[i] = 0; res[0] = 1; while ((1ll << pnt) <= n) pnt++; for (int p = pnt; p >= 0; p--) { mul(res,res,k); if ((n >> p) & 1) { for (int i = k - 1; i >= 0; i--) res[i + 1] = res[i]; res[0] = 0; rep(j,SZ(Md)) res[Md[j]] = (res[Md[j]] - res[k] * _md[Md[j]]) % mod; } } rep(i,k) ans = (ans + res[i] * b[i]) % mod; if (ans<0) ans += mod; return ans; } VI BM(VI s) { VI C(1,1),B(1,1); int L = 0,m = 1,b = 1; rep(n,0,SZ(s)) { ll d = 0; rep(i,L + 1) d = (d + (ll)C[i] * s[n - i]) % mod; if (d == 0) ++m; else if (2 * L <= n) { VI T = C; ll c = mod - d * powmod(b,mod - 2) % mod; while (SZ(C)<SZ(B) + m) C.pb(0); rep(i,SZ(B)) C[i + m] = (C[i + m] + c * B[i]) % mod; L = n + 1 - L; B = T; b = d; m = 1; } else { ll c = mod - d * powmod(b,SZ(B)) C[i + m] = (C[i + m] + c * B[i]) % mod; ++m; } } return C; } int gao(VI a,ll n) { VI c = BM(a); c.erase(c.begin()); rep(i,SZ(c)) c[i] = (mod - c[i]) % mod; return solve(n,c,VI(a.begin(),a.begin() + SZ(c))); }};int main() { cin >> n; vector<int> V; int a[] = {3,9,20,40,85,191,426,931,2028,4444,9765,21430,46970}; for(int i = 0; i <= 12; i++) V.push_back(a[i]); printf("%lld\n",1ll * linear_seq::gao(V,n - 1)%mod);}总结
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