add single function for mod division

Author: lrvideckis

library/math/mod_division.hpp

@@ -0,0 +1,8 @@
+#pragma once
+const int mod = 998244353;
+int mod_div(int x, int y) {
+  int m = mod, u = 1, v = 0;
+  while (m) swap(u -= y / m * v, v), swap(y %= m, m);
+  assert(y == 1);
+  return 1LL * x * (u + mod) % mod;
+}

library/math/mod_int.hpp

@@ -0,0 +1,21 @@
+#define PROBLEM \
+  "https://onlinejudge.u-aizu.ac.jp/problems/ITP1_1_A"
+#include "../template.hpp"
+#define const ;
+#include "../../../library/math/mod_division.hpp"
+#undef const
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  for (mod = 1; mod < 500; mod++) {
+    for (int x = 0; x < mod; x++) {
+      for (int y = 0; y < mod; y++) {
+        if (gcd(y, mod) == 1) {
+          int quotient = mod_div(x, y);
+          assert(1LL * quotient * y % mod == x);
+        }
+      }
+    }
+  }
+  cout << "Hello World\n";
+  return 0;
+}