Merge pull request matthewsamuel95#903 from 3agwa/add-wilson's-theorem-to-math

Update Math/Wilson's Theorem/Wilson's Theorem.cpp

Author: matthewsamuel95

Math/Wilson's Theorem/Wilson's Theorem.cpp

@@ -0,0 +1,75 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+typedef long long ll;
+typedef long double ld;
+typedef vector<int> vi;
+typedef vector<vector<int> > vvi;
+typedef pair<int, int> pii;
+
+#define erep(i, x, n) for (auto i = x; i<=(ll)(n); i++)
+#define rep(i, x, n) for(auto i = x; i<(ll)(n); i++)
+#define all(v) ((v).begin()), ((v).end())
+#define sz(v) ((int)((v).size()))
+#define mod(n, m) ((n%m + m) % m)
+#define reset(n, m) memset(n, m, sizeof n)
+#define endl '\n'
+
+int power(int x, unsigned int y, int p)
+{
+	int res = 1; // Initialize result
+	x = x % p; // Update x if it is more than or
+	// equal to p
+	while (y > 0)
+	{
+		// If y is odd, multiply x with result
+		if (y & 1)
+			res = (res * 1ll * x) % p;
+
+		// y must be even now
+		y = y >> 1; // y = y/2
+		x = (x * 1ll * x) % p;
+	}
+	return res;
+}
+
+// Function to find modular inverse of a under modulo p
+// using Fermat's method. Assumption: p is prime
+int modInverse(int a, int p)
+{
+	return power(a, p - 2, p);
+}
+
+// Returns n! % p using Wilson's Theorem
+int modFact(int n, int p)
+{
+	// n! % p is 0 if n >= p
+	if (p <= n)
+		return 0;
+
+	// Initialize result as (p-1)! which is -1 or (p-1)
+	int res = (p - 1), den = 1;
+
+	// Multiply modulo inverse of all numbers from (n+1)
+	// to p
+	for (int i = n + 1; i < p; i++)
+		res = (res * 1ll * i) % p;
+	return res * modInverse(den, p - 2);
+}
+
+int main()
+{
+	ios_base::sync_with_stdio(0);
+	cin.tie(0);
+
+	int tc;
+	cin >> tc;
+	while (tc--)
+	{
+		int n, m;
+		cin >> n >> m;
+		cout << modFact(n, m) << endl;
+	}
+	return 0;
+}