2023 rcpc

2023/rcpc/d2/editorial/i-ksumt-67.cpp

@@ -0,0 +1,102 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <cassert>
+#warning That's the baby, that's not my baby
+
+typedef long long ll;
+
+
+/**
+
+b[0] = a[1] = a[t + 1] = a[2 * t + 1] = ...
+b[1] = a[2] = a[t + 2] = a[2 * t + 2] = ...
+b[2] = a[3] = a[t + 3] = a[2 * t + 3] = ...
+
+b[0] * x + b[1] * x + ... + b[i] * x + b[i + 1] * (x - 1) + b[i + 2] * (x - 1) + ...  b[t - 1] * (x - 1) = s
+
+x * (b[0] + b[1] + ... + b[i]) + (x - 1) * (b[i + 1] + b[i + 2] + ... + b[t - 1]) = s
+
+i = k % t, x = k / t + 1
+
+x * a + b * (x - 1) = s
+
+**/
+
+const int mod = 1e9 + 7;
+const int NMAX = 1e7;
+
+int fac[NMAX + 1], ifac[NMAX + 1];
+
+int power(int a, int b) {
+  int p = 1;
+  while (b) {
+    if (b & 1) {
+      p = (ll) p * a % mod;
+    }
+    a = (ll) a * a % mod;
+    b >>= 1;
+  }
+  return p;
+}
+
+int C(int n, int k) {
+  if (n < k) {
+    return 0;
+  }
+  return (ll) fac[n] * ifac[k] % mod * ifac[n - k] % mod;
+}
+
+int sb(int n, int k) {
+  return C(k - 1, n - 1);
+}
+
+int main() {
+  fac[0] = 1;
+  for (int i = 1; i <= NMAX; i++) {
+    fac[i] = (ll) fac[i - 1] * i % mod;
+  }
+  ifac[NMAX] = power(fac[NMAX], mod - 2);
+  for (int i = NMAX - 1; i >= 0; i--) {
+    ifac[i] = (ll) ifac[i + 1] * (i + 1) % mod;
+  }
+  for (int i = 0; i <= NMAX; i++) {
+    assert((ll) fac[i] * ifac[i] % mod == 1);
+  }
+
+  int k, s, t;
+  std::cin >> k >> s >> t;
+
+  int i = k % t, x = k / t + 1; // x >= 2
+
+  if (i == 0) {
+    if (s % (x - 1) != 0) {
+      std::cout << 0;
+    } else {
+      std::cout << sb(t, s / (x - 1));
+    }
+    return 0;
+  }
+
+  /// x * a + b * (x - 1) = s
+
+  int answer = 0;
+
+  for (int a = 0; a * x <= s; a++) {
+    int b = s - a * x;
+    if (b % (x - 1) != 0) {
+      continue;
+    }
+    b /= x - 1;
+    /// a = suma primelor i, b = suma ultimelor t - i
+    answer += (ll) sb(i, a) * sb(t - i, b) % mod;
+
+    if (answer >= mod) {
+      answer -= mod;
+    }
+  }
+
+  std::cout << answer;
+
+  return 0;
+}