Problem: You are given a connected graph with N vertices and M edges. The vertices are numbered 1 to N. The i-th edge is an undirected edge of length C_i connecting Vertex A_i and Vertex B_i.

Additionally, an odd number MOD is given.

You will be given Q queries, which should be processed. The queries take the following form:

* Given in the i-th query are S_i, T_i and R_i. Print `YES` if there exists a path from Vertex S_i to Vertex T_i whose length is R_i modulo MOD, and print `NO` otherwise. A path may traverse the same edge multiple times, or go back using the edge it just used.



Here, in this problem, the length of a path is NOT the sum of the lengths of its edges themselves, but the length of the first edge used in the path gets multiplied by 1, the second edge gets multiplied by 2, the third edge gets multiplied by 4, and so on. (More formally, let L_1,...,L_k be the lengths of the edges used, in this order. The length of that path is the sum of L_i \times 2^{i-1}.)

Constraints

* 1 \leq N,M,Q \leq 50000
* 3 \leq MOD \leq 10^{6}
* MOD is odd.
* 1 \leq A_i,B_i\leq N
* 0 \leq C_i \leq MOD-1
* 1 \leq S_i,T_i \leq N
* 0 \leq R_i \leq MOD-1
* The given graph is connected. (It may contain self-loops or multiple edges.)

Input

Input is given from Standard Input in the following format:


N M Q MOD
A_1 B_1 C_1
\vdots
A_M B_M C_M
S_1 T_1 R_1
\vdots
S_Q T_Q R_Q


Output

Print the answers to the i-th query in the i-th line.

Examples

Input

3 2 2 2019
1 2 1
2 3 2
1 3 5
1 3 4


Output

YES
NO


Input

6 6 3 2019
1 2 4
2 3 4
3 4 4
4 5 4
5 6 4
6 1 4
2 6 1110
3 1 1111
4 5 1112


Output

YES
NO
NO


Input

1 2 3 25
1 1 1
1 1 2
1 1 13
1 1 6
1 1 14


Output

YES
YES
YES


Input

10 15 10 15
1 2 1
2 3 6
3 4 6
2 5 1
5 6 1
4 7 6
1 8 11
2 9 6
5 10 11
9 10 11
3 6 1
2 5 1
2 7 11
9 10 11
5 6 11
1 3 5
9 8 3
7 7 7
7 10 13
4 1 10
9 3 12
10 10 14
9 2 1
6 6 5
8 8 4


Output

YES
NO
NO
NO
NO
NO
NO
YES
YES
NO

Solution (in JAVA):

Solution:
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Math.abs;
import static java.lang.System.exit;
import static java.util.Arrays.fill;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	static class Edge {
		final int to, len;

		Edge(int to, int len) {
			this.to = to;
			this.len = len;
		}
	}

	static List<Edge> edges[];
	static int mod, npows, pows[];
	static int mapPow[], mapAdd[], mapAddBack[];

	static void solve() throws Exception {
		int n = scanInt();
		int m = scanInt();
		int q = scanInt();
		mod = scanInt();
		edges = new List[n];
		for (int i = 0; i < n; i++) {
			edges[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int a = scanInt() - 1, b = scanInt() - 1, c = scanInt();
			edges[a].add(new Edge(b, c));
			edges[b].add(new Edge(a, c));
		}
		for (int i = 1, pow = 2;; i++, pow = (2 * pow) % mod) {
			if (pow == 1) {
				npows = i;
				break;
			}
		}
		pows = new int[npows + 1];
		for (int i = 0, pow = 1; i <= npows; i++, pow = (2 * pow) % mod) {
			pows[i] = pow;
		}
		mapPow = new int[n];
		mapAdd = new int[n];
		mapAddBack = new int[n];
		fill(mapPow, -1);
		dfs(0, 0, 0, 0);
		int mod2 = mod;
		int zeroAdds[] = new int[npows];
		fill(zeroAdds, -1);
		zeroAdds[0] = 0;
		for (int i = 0; i < n; i++) {
			int curPow = mapPow[i], curAdd = mapAdd[i];
			for (Edge e: edges[i]) {
				int curPow2 = (curPow + 1 + mapPow[e.to]) % npows,
				    curAdd2 = (int) (((long) (2 * curAdd + e.len) * pows[mapPow[e.to]] + mapAddBack[e.to]) % mod);
				if (zeroAdds[curPow2] >= 0) {
					mod2 = gcd(mod2, abs(zeroAdds[curPow2] - curAdd2));
				} else {
					zeroAdds[curPow2] = curAdd2;
				}
			}
		}
		if (npows > 2 && zeroAdds[1] < 0 && zeroAdds[2] < 0) {
			throw new AssertionError();
		}
		if (npows % 2 != 0 && zeroAdds[1] < 0) {
			for (int i = 3; i < npows; i += 2) {
				if (zeroAdds[i] >= 0) {
					int curPow = (i + 2) % npows,
					    curAdd = (zeroAdds[i] * 4 + zeroAdds[2]) % mod;
					if (zeroAdds[curPow] >= 0) {
						mod2 = gcd(mod2, abs(zeroAdds[curPow] - curAdd));
					} else {
						zeroAdds[curPow] = curAdd;
					}
				}
			}
		}
		if (npows > 2 || zeroAdds[1] >= 0) {
			for (int i = 0; i < npows; i++) {
				if (zeroAdds[i] < 0) {
					continue;
				}
				int curPow, curAdd;
				if (zeroAdds[1] >= 0) {
					curPow = (i + 1) % npows;
					curAdd = (2 * zeroAdds[i] + zeroAdds[1]) % mod;
				} else {
					curPow = (i + 2) % npows;
					curAdd = (4 * zeroAdds[i] + zeroAdds[2]) % mod;
				}
				if (zeroAdds[curPow] >= 0) {
					mod2 = gcd(mod2, abs(zeroAdds[curPow] - curAdd));
				} else {
					zeroAdds[curPow] = curAdd;
				}
			}
		}
		int groups[] = new int[mod2];
		fill(groups, -1);
		int ngroups = 0;
		for (int i = 0; i < mod2; i++) {
			if (groups[i] >= 0) {
				continue;
			}
			for (int j = i;;) {
				groups[j] = ngroups;
				if (zeroAdds[1] >= 0) {
					j = (2 * j + zeroAdds[1]) % mod2;
				} else if (npows > 2) {
					j = (4 * j + zeroAdds[2]) % mod2;
				}
				if (j == i) {
					break;
				}
			}
			++ngroups;
		}
		for (int qq = 0; qq < q; qq++) {
			int s = scanInt() - 1, t = scanInt() - 1, r = scanInt();
			int v1 = mapAddBack[t] % mod2;
			int v2 = (int) ((long) (r + mod - mapAdd[s]) * pows[npows - mapPow[s]] % mod2);
			out.println(groups[v1] == groups[v2] ? "YES" : "NO");
		}
	}

	static void dfs(int cur, int curPow, int curAdd, int curAddBack) {
		mapPow[cur] = curPow;
		mapAdd[cur] = curAdd;
		mapAddBack[cur] = curAddBack;
		for (Edge e: edges[cur]) {
			if (mapPow[e.to] >= 0) {
				continue;
			}
			dfs(e.to, (curPow + 1) % npows, (curAdd * 2 + e.len) % mod, (int) ((curAddBack + (long) e.len * pows[curPow]) % mod));
		}
	}

	static int scanInt() throws IOException {
		return parseInt(scanString());
	}

	static long scanLong() throws IOException {
		return parseLong(scanString());
	}

	static String scanString() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	public static void main(String[] args) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			exit(1);
		}
	}
}