矩陣快速冪

轉移矩陣很容易看出來，關鍵是p/i怎么處理。。

其實是有規律的。。第i項的p/i是x，那么第p / (p / i)項也是x。。且中間全是x。。

然后分段轉移就行了

#include <bits/stdc++.h> #define INF 0x3f3f3f3f #define full(a, b) memset(a, b, sizeof a) #define FAST_IO ios::sync_with_stdio(false), cin.tie(0), cout.tie(0) using namespace std; typedef long long ll; inline int lowbit(int x){ return x & (-x); } inline int read(){int X = 0, w = 0; char ch = 0;while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();return w ? -X : X; } inline int gcd(int a, int b){ return b ? gcd(b, a % b) : a; } inline int lcm(int a, int b){ return a / gcd(a, b) * b; } template<typename T> inline T max(T x, T y, T z){ return max(max(x, y), z); } template<typename T> inline T min(T x, T y, T z){ return min(min(x, y), z); } template<typename A, typename B, typename C> inline A fpow(A x, B p, C lyd){A ans = 1;for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;return ans; } const int MOD = 1e9 + 7; ll a, b, c, d, p, n, _; struct Matrix{ll m[3][3];Matrix(){full(m, 0);} }; Matrix e;Matrix mul(Matrix &p, Matrix &q){Matrix ret;for(int i = 0; i < 3; i ++){for(int j = 0; j < 3; j ++){for(int k = 0; k < 3; k ++){ret.m[i][j] = (ret.m[i][j] % MOD + p.m[i][k] * q.m[k][j] % MOD) % MOD;}}}return ret; }Matrix fpow(Matrix &x, ll p){Matrix ret = e;for(; p; p >>= 1, x = mul(x, x)){if(p & 1) ret = mul(ret, x);}return ret; }int main(){FAST_IO;for(cin >> _; _; _ --){cin >> a >> b >> c >> d >> p >> n;e.m[0][0] = 1, e.m[1][1] = 1, e.m[2][2] = 1;if(n == 1) printf("%lld\n", a % MOD);else if(n == 2) printf("%lld\n", b % MOD);else{bool good = false;Matrix tmp;tmp.m[0][0] = d, tmp.m[0][1] = c, tmp.m[1][0] = 1, tmp.m[2][2] = 1;for(int i = 3; i <= n;){if(p / i == 0){Matrix t = tmp;t = fpow(t, n - i + 1);ll ans = (t.m[0][0] * b % MOD + t.m[0][1] * a % MOD + t.m[0][2]) % MOD;printf("%lld\n", ans);good = true;break;}else{Matrix t = tmp;t.m[0][2] = p / i;int j = min(n, p / (p / i));t = fpow(t, j - i + 1);ll nb = (t.m[0][0] * b % MOD + t.m[0][1] * a % MOD + t.m[0][2]) % MOD;ll na = (t.m[1][0] * b % MOD + t.m[1][1] * a % MOD + t.m[1][2]) % MOD;a = na, b = nb;i = j + 1;}}if(!good) printf("%lld\n", b % MOD);}}return 0; }

轉載于:https://www.cnblogs.com/onionQAQ/p/10946324.html

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