add exgcd template

Author: Clouder0

templates/exgcd.cpp

@@ -1,5 +1,42 @@
-void exgcd(int a, int b, int& x, int& y)
+#include <cstdio>
+#define int long long
+
+int exgcd(int a, int b, int& x, int& y)
 {
-    if (b == 0) return (void)(x = 1, y = 0);
-    exgcd(b, a % b, y, x), y -= (a / b) * x;
+    if (b == 0) return x = 1, y = 0, a;
+    int ret = exgcd(b, a % b, y, x);
+    y -= (a / b) * x;
+    return ret;
+}
+
+bool linearEquation(int a, int& x, int b, int& y, int c)
+{
+    int g = exgcd(a, b, x, y);
+    if (c % g) return false;
+    int scale = c / g;
+    x = x * scale;
+    y = y * scale;
+    // x minimum positive root
+    int mod = b / g;
+    x = x % mod;
+    if (x <= 0) x += mod;
+    y = (c - a * x) / b;
+    return true;
+}
+
+int LinearModEquation(int a, int& x, int b, int p)
+{
+    int y;
+    linearEquation(a, x, p, y, b);
+    return x % p;
+}
+
+int a, b;
+signed main()
+{
+    scanf("%lld%lld",&a,&b);
+    int x, y;
+    linearEquation(a, x, b, y, 1);
+    printf("%lld\n", x);
+    return 0;
 }