Merge pull request #714 from AlgorithmWithGod/khj20006

[20250822] BOJ / P5 / (Relatively) Prime / 권혁준

Author: ShinHeeEul

khj20006/202508/22 BOJ P5 (Relatively) Prime.md

@@ -0,0 +1,111 @@
+```java
+import java.awt.image.AreaAveragingScaleFilter;
+import java.util.*;
+import java.io.*;
+
+class IOController {
+	BufferedReader br;
+	BufferedWriter bw;
+	StringTokenizer st;
+
+	public IOController() {
+		br = new BufferedReader(new InputStreamReader(System.in));
+		bw = new BufferedWriter(new OutputStreamWriter(System.out));
+		st = new StringTokenizer("");
+	}
+
+	String nextLine() throws Exception {
+		String line = br.readLine();
+		st = new StringTokenizer(line);
+		return line;
+	}
+
+	String nextToken() throws Exception {
+		while (!st.hasMoreTokens()) nextLine();
+		return st.nextToken();
+	}
+
+	int nextInt() throws Exception {
+		return Integer.parseInt(nextToken());
+	}
+
+	long nextLong() throws Exception {
+		return Long.parseLong(nextToken());
+	}
+
+	double nextDouble() throws Exception {
+		return Double.parseDouble(nextToken());
+	}
+
+	void close() throws Exception {
+		bw.flush();
+		bw.close();
+	}
+
+	void write(String content) throws Exception {
+		bw.write(content);
+	}
+
+}
+
+public class Main {
+
+	static IOController io;
+
+	//
+
+	static final long MOD = 998244353;
+	static long P, N, M;
+
+	public static void main(String[] args) throws Exception {
+
+		io = new IOController();
+
+		for(int T=io.nextInt(); T-->0; ) {
+			init();
+			solve();
+		}
+
+		io.close();
+
+	}
+
+	static void init() throws Exception {
+
+		P = io.nextLong();
+		N = io.nextLong();
+		M = io.nextLong();
+
+	}
+
+	static void solve() throws Exception {
+
+		if(N < M) {
+			long t = N;
+			N = M;
+			M = t;
+		}
+
+		long pm = power(P, M);
+		long ans = pm * ((power(pm, N/M) + MOD - 1) % MOD) % MOD;
+		ans = (ans * (power((pm+MOD-1)%MOD, MOD-2))) % MOD;
+		if(N%M != 0) ans = (ans + power(P, N)) % MOD;
+
+		if(pm == 1) {
+			ans = N/M;
+			if(N%M != 0) ans = (ans + power(P, N)) % MOD;
+		}
+		io.write(ans + "\n");
+
+	}
+
+	static long power(long a, long x) {
+		if(x == 0) return 1;
+		if(x == 1) return a%MOD;
+		long h = power(a, x>>1) % MOD;
+		if(x%2 == 0) return h*h%MOD;
+		return h*h%MOD*a%MOD;
+	}
+
+}
+```