P4031 [Code+#2]可做题2

https://www.luogu.com.cn/record/94434461

Luogu/P4031/P4031.cpp

@@ -0,0 +1,120 @@
+#include <iostream>
+#include <algorithm>
+#include <cstring>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+class Matrix {
+  private:
+    long long data[10][10], mod;
+
+  public:
+    Matrix(long long _mod = 1e9 + 7)
+        : mod(_mod) {
+        memset(data, 0x00, sizeof(data));
+    }
+
+    long long *operator[](long long i) {
+        return data[i];
+    }
+
+    Matrix operator*(Matrix b) const {
+        Matrix c(mod);
+
+        int n = 2;
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= n; j++) {
+                for (int k = 1; k <= n; k++) {
+                    c[i][j] = (c[i][j] + data[i][k] * b[k][j] % mod) % mod;
+                }
+            }
+        }
+
+        return c;
+    }
+};
+
+Matrix binpow(Matrix a, long long k, long long p) {
+    Matrix res(p);
+    res[1][1] = 1;
+    res[1][2] = 1;
+
+    while (k) {
+        if (k & 1) res = res * a;
+        a = a * a;
+        k >>= 1;
+    }
+
+    return res;
+}
+
+long long fib(long long n, long long p) {
+    if (n <= 2) {
+        return n != 0;
+    }
+
+    Matrix tmp(p);
+
+    tmp[1][1] = 1, tmp[1][2] = 1;
+    tmp[2][1] = 1, tmp[2][2] = 0;
+
+    return binpow(tmp, n - 2, p)[1][1];
+}
+
+long long exgcd(long long a, long long b, long long &x, long long &y) {
+    if (!b) {
+        x = 1, y = 0;
+        return a;
+    }
+
+    long long g = exgcd(b, a % b, y, x);
+    y -= a / b * x;
+
+    return g;
+}
+
+long long calc(long long x, long long y) {
+    if (x == 0) return 0;
+
+    return x < 0 ? -(-x + y - 1) / y : x / y;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int t;
+
+    cin >> t;
+
+    while (t--) {
+        long long i, l, r, k, p, m, x, y;
+
+        cin >> i >> l >> r >> k >> p >> m;
+
+        long long f1 = fib(k - 2, p),
+                  f2 = fib(k - 1, p);
+
+        long long a = f2,
+                  b = p,
+                  c = ((m - i % p * f1 % p) + p) % p,
+                  g = std::__gcd(a, b);
+
+        if (c % g) {
+            cout << 0 << endl;
+
+            continue;
+        }
+
+        a /= g, b /= g, c /= g;
+        exgcd(a, b, x, y);
+        x = (x * c % b + b) % b;
+
+        cout << calc(r - x, b) - calc(l - x - 1, b) << endl;
+    }
+
+    return 0;
+}