new file: P15569.cpp

P15569.cpp

@@ -0,0 +1,88 @@
+#include <bits/stdc++.h>
+using namespace std;
+const int mod = 1e9 + 7;
+int n, k;
+namespace mat {
+struct Mat {
+    long long a[3][3];
+    int n, m;
+    Mat(int _n = 0, int _m = 0) : n(_n), m(_m) { memset(a, 0, sizeof(a)); }
+    void operator*=(const Mat &b) {
+        if (m != b.n) {
+            exit(-1);
+        }
+        long long res[105][105] = {};
+        for (int i = 1; i <= n; ++i) {
+            for (int j = 1; j <= b.m; ++j) {
+                for (int k = 1; k <= m; ++k) {
+                    res[i][j] = (res[i][j] + a[i][k] * b.a[k][j]) % mod;
+                }
+            }
+        }
+        for (int i = 1; i <= n; ++i) {
+            for (int j = 1; j <= b.m; ++j) {
+                a[i][j] = res[i][j];
+            }
+        }
+        m = b.m;
+    }
+};
+Mat qpow(Mat a, long long k) {
+    Mat res(a.n, a.n);
+    for (int i = 1; i <= a.n; ++i) {
+        res.a[i][i] = 1;
+    }
+    while (k) {
+        if (k & 1)
+            res *= a;
+        a *= a;
+        k >>= 1;
+    }
+    return res;
+}
+long long f(int n) {
+    if (n <= 1) {
+        return 1;
+    }
+    Mat base1(1, 2), base2(2, 2);
+    base1.a[1][1] = 1;
+    base1.a[1][2] = 1;
+    base2.a[1][1] = 1;
+    base2.a[1][2] = 1;
+    base2.a[2][1] = 1;
+    base2.a[2][2] = 0;
+    base2 = mat::qpow(base2, n - 1);
+    base1 *= base2;
+    return base1.a[1][1];
+}
+} // namespace mat
+long long qpow(long long a, long long b) {
+    a %= mod;
+    long long res = 1;
+    while (b) {
+        if (b & 1)
+            res = (res * a) % mod;
+        a = (a * a) % mod;
+        b >>= 1;
+    }
+    return res;
+}
+long long ni(int a) { return qpow(a, mod - 2); }
+int main() {
+    scanf("%d%d", &n, &k);
+    if (k < n) {
+        printf("0\n");
+        return 0;
+    }
+    long long all = qpow(k, n);
+    long long correct = mat::f(n);
+    printf("%lld\n", (correct * ni(all)) % mod);
+    // printf("%lld\n", mat::f(n + 1));
+    return 0;
+}
+/*
+排列
+0 <= ai + i - n <= 2
+n - i <= ai <= 2 + n - i
+只能取 n - i, n - i + 1, n - i + 2 三种
+*/