Submission #929959

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Source Code Expand

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni(), m = ni(), K = ni();
		int[] from = new int[m];
		int[] to = new int[m];
		int[] w = new int[m];
		for(int i = 0;i < m;i++){
			from[i] = ni()-1;
			to[i] = ni()-1;
			w[i] = i;
		}
		int[][][] g = packWU(n, from, to, w);
		BCDatum bcd = decomposeToBiconnectedComponents(g);
		int[][] cb = makeBuckets(bcd.edgeClus);
		
		int mod = 1000000007;
		long[][] C = new long[1000 + 1][1000 + 1];
		for (int i = 0; i <= 1000; i++) {
			C[i][0] = 1;
			for (int j = 1; j <= i; j++) {
				C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
				if (C[i][j] >= mod)
					C[i][j] -= mod;
			}
		}

		long ret = 1;
		for(int[] row : cb){
			if(row.length == 0)continue;
			int[] ap = new int[row.length*2];
			int p = 0;
			for(int v : row){
				ap[p++] = from[v];
				ap[p++] = to[v];
			}
			Arrays.sort(ap);
			int uv = 0;
			for(int i = 0;i < ap.length;i++){
				if(i == 0 || ap[i] != ap[i-1]){
					uv++;
				}
			}
			if(uv > row.length){
				ret = ret * pow(K, row.length, mod) % mod;
			}else if(uv == row.length){
				long res = 0;
				for(int i = 1;i <= uv;i++){
					int gg = gcd(uv, i);
					res += pow(K, gg, mod);
				}
				ret = ret * (res % mod * invl(uv, mod) % mod) % mod;
			}else{
				ret = ret * C[row.length+K-1][K-1] % mod;
			}
		}
		out.println(ret);
	}
	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}

	
	public static int gcd(int a, int b) {
		while (b > 0) {
			int c = a;
			a = b;
			b = c % b;
		}
		return a;
	}
	
	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}

	
	public static int[][] makeBuckets(int[] a)
	{
		int n = a.length;
		int sup = 0;
		for(int v : a)sup = Math.max(sup, v);
		int[][] bucket = new int[sup+1][];
		int[] bp = new int[sup+1];
		for(int i = 0;i < n;i++)bp[a[i]]++;
		for(int i = 0;i <= sup;i++)bucket[i] = new int[bp[i]];
		for(int i = n-1;i >= 0;i--)bucket[a[i]][--bp[a[i]]] = i;
		return bucket;
	}

	
	public static BCDatum decomposeToBiconnectedComponents(int[][][] g)
	{
		int n = g.length;
		int m = 0;
		for(int[][] row : g)m += row.length;
		m /= 2;
		BCDatum d = new BCDatum();
		d.g = g;
		d.gen = 0;
		d.low = new int[n];
		Arrays.fill(d.low, -1);
		d.ord = new int[n];
		Arrays.fill(d.ord, -1);
		d.edgeStack = new int[m];
		d.esp = 0;
		d.edgeClus = new int[m];
		Arrays.fill(d.edgeClus, -1);
		d.visited = new boolean[n];
		d.parente = new int[n];
		d.isArtic = new boolean[n];
		Arrays.fill(d.parente, -1);
		for(int i = 0;i < n;i++){
			if(!d.visited[i])dfsBC(i, d);
		}
		assert d.esp == 0;
		return d;
	}
	
	private static void dfsBC(int cur, BCDatum d)
	{
		d.visited[cur] = true;
		d.low[cur] = d.ord[cur] = d.gen++;
		int dfsch = 0;
		for(int[] e : d.g[cur]){
			if(!d.visited[e[0]]){
				d.edgeStack[d.esp++] = e[1];
				d.parente[e[0]] = e[1];
				dfsch++;
				dfsBC(e[0], d);
				if(d.low[e[0]] >= d.ord[cur]){
					d.isArtic[cur] = true;
					while(d.esp > 0){
						d.edgeClus[d.edgeStack[--d.esp]] = d.ecp;
						if(d.edgeStack[d.esp] == e[1])break;
					}
					d.ecp++;
				}
				d.low[cur] = Math.min(d.low[cur], d.low[e[0]]);
			}else if(d.parente[cur] != e[1] && d.ord[e[0]] < d.ord[cur]){
				// e is a back edge from cur to its ancestor e[0]
				d.edgeStack[d.esp++] = e[1];
				d.low[cur] = Math.min(d.low[cur], d.ord[e[0]]);
			}
		}
		if(d.parente[cur] < 0 && dfsch == 1)d.isArtic[cur] = false; // if root node and degree on dfs tree = 1 then not articulation point.
	}
	
	public static class BCDatum
	{
		public int[][][] g;
		public int[] edgeClus;
		public int ecp;
		public int gen;
		public int[] ord;
		public int[] low;
		public int[] edgeStack;
		public int esp;
		public boolean[] visited;
		public int[] parente;
		public boolean[] isArtic;
	}
	
	public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
		int[][][] g = new int[n][][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int t : to)
			p[t]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]][2];
		for (int i = 0; i < from.length; i++) {
			--p[from[i]];
			g[from[i]][p[from[i]]][0] = to[i];
			g[from[i]][p[from[i]]][1] = w[i];
			--p[to[i]];
			g[to[i]][p[to[i]]][0] = from[i];
			g[to[i]][p[to[i]]][1] = w[i];
		}
		return g;
	}


	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}

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