[20250306] BOJ / P3 / N!!!...! mod P / 권혁준

khj20006/202503/06 BOJ P3 N!!!...! mod P.md

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+```java
+
+#include <iostream>
+using namespace std;
+using ll = long long;
+
+ll N, K, P;
+
+ll power(ll n, ll m){
+    if(m == 0) return 1;
+    if(m == 1) return n;
+    ll p = power(n,m>>1);
+    if(m&1) return p*p%P*n%P;
+    return p*p%P;
+}
+
+int main() {
+	cin.tie(0)->sync_with_stdio(0);
+
+	cin >> N >> K >> P;
+
+	if (N == 2) return cout << (P == 2 ? 0 : 2), 0;
+
+	if (K >= 4) return cout << 0, 0;
+
+	if (K == 2) {
+		if (N >= 13) return cout << 0, 0;
+        ll fac = 1;
+        for (int i = 1; i <= N; i++) fac *= i;
+        if (fac >= P) return cout << 0, 0;
+        if(N <= 11){
+            ll ans = 1;
+            for(int i=2;i<=fac;i++) ans = (ans * i) % P;
+            return cout<<ans,0;
+        }
+
+        ll res = 1;
+        for(int i=479001601;i<P;i++) res = (res * i) % P;
+
+        cout<<(P-1) * power(res,P-2) % P;
+
+	}
+
+	if (K == 3) {
+		if (N >= 4) return cout << 0, 0;
+		ll ans = 1;
+		for (int i = 1; i <= 720; i++) ans = (ans * i) % P;
+		cout << ans;
+	}
+
+}
+
+```