Problem: We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.

The i-th edge connects Vertex U_i and Vertex V_i. The time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).

Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible. Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.

Constraints

* 1 \leq N \leq 100 000
* 1 \leq M \leq 200 000
* 1 \leq S, T \leq N
* S \neq T
* 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
* 1 \leq D_i \leq 10^9 (1 \leq i \leq M)
* If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
* U_i \neq V_i (1 \leq i \leq M)
* D_i are integers.
* The given graph is connected.

Input

Input is given from Standard Input in the following format:


N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M


Output

Print the answer.

Examples

Input

4 4
1 3
1 2 1
2 3 1
3 4 1
4 1 1


Output

2


Input

3 3
1 3
1 2 1
2 3 1
3 1 2


Output

2


Input

8 13
4 2
7 3 9
6 2 3
1 6 4
7 6 9
3 8 9
1 2 2
2 8 12
8 6 9
2 5 5
4 2 18
5 3 7
5 1 515371567
4 8 6


Output

6

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedInputStream;
import java.lang.reflect.Array;
import java.io.BufferedWriter;
import java.util.PriorityQueue;
import java.util.InputMismatchException;
import java.io.FileInputStream;
import java.util.function.Supplier;
import java.util.ArrayList;
import java.util.List;
import java.util.AbstractCollection;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author jasonsun0310
 */
public class Main {
	public static void main(String[] args)
	{
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		E solver = new E();
		solver.solve(1, in, out);
		out.close();
	}

	static @SuppressWarnings("ALL")
	class E {
		private static final int    MOD          = (int) (1e9+7);
		private static final int    MAXN         = 100000+5;
		private              long[] distS        = new long[MAXN];
		private              long[] distT        = new long[MAXN];
		private              int[]  waysS        = new int[MAXN];
		private              int[]  waysT        = new int[MAXN];
		private              int[]  waysShortest = new int[MAXN];

		public void solve(int testNumber, InputReader in, OutputWriter out)
		{
			int n = in.readInt();
			List<Edge>[] edges = ArrayUtils.array(n, () -> new ArrayList<>());
			int m = in.readInt();
			int s = in.readInt()-1;
			int t = in.readInt()-1;
			for(int i = 0; i < m; i++)
			{
				int a = in.readInt()-1;
				int b = in.readInt()-1;
				int c = in.readInt();
				edges[a].add(new Edge(b, c));
				edges[b].add(new Edge(a, c));
			}
			ArrayUtils.fill(distS, 0, n, 0); ArrayUtils.fill(distT, 0, n, 0);
			ArrayUtils.fill(waysS, 0, n, 0); ArrayUtils.fill(waysT, 0, n, 0);
			ArrayUtils.fill(waysShortest, 0, n, 0);
			dijkstra(s, edges, distS, waysS); dijkstra(t, edges, distT, waysT);
			for(int i = 0; i < n; i++)
			{
				if(distS[i]+distT[i] != distS[t]) continue;
				waysShortest[i] = (int) ((long) waysS[i]*waysT[i]%MOD);
			}

			long ans = (long) waysShortest[t]*waysShortest[t]%MOD;
			for(int i = 0; i < n; i++)
			{
				if(distS[i]+distT[i] != distS[t]) continue;
				if(distS[i] == distT[i])
				{
					ans = (ans-(long) waysShortest[i]*waysShortest[i])%MOD;
					if(ans < 0) ans += MOD;
				}
			}
			// Do not meet on an edge.
			for(int i = 0; i < n; i++)
			{
				for(Edge e : edges[i])
				{
					int j = e.dst;
					if(distS[i]+e.length+distT[j] != distS[t])
						continue;
					long l1 = distS[i];
					long r1 = distS[j];
					long l2 = distT[j];
					long r2 = distT[i];
					if(Math.max(l1, l2) < Math.min(r1, r2))
					{
						long cur = (long) waysS[i]*waysT[j]%MOD*waysS[i]%MOD*waysT[j]%MOD;
						ans -= cur;
						if(ans < 0) ans += MOD;
					}
				}
			}

			out.printLine(ans);
		}

		private long[] dijkstra(int s, List<Edge>[] edges, long[] dist, int[] ways)
		{
			final long infinity = Long.MAX_VALUE/2;
			Arrays.fill(dist, infinity);
			dist[s] = 0;
			ways[s] = 1;
			PriorityQueue<Vertex> pq = new PriorityQueue<>();
			pq.offer(new Vertex(s, 0));
			while(!pq.isEmpty())
			{
				Vertex ver = pq.poll();
				int v = ver.v;
				if(ver.dist != dist[v]) continue;
				for(Edge e : edges[v])
				{
					int u = e.dst;
					if(dist[u] > dist[v]+e.length)
					{
						dist[u] = dist[v]+e.length;
						ways[u] = ways[v];
						pq.offer(new Vertex(u, dist[u]));
					}
					else if(dist[u] == dist[v]+e.length)
					{
						ways[u] += ways[v];
						if(ways[u] >= MOD) ways[u] -= MOD;
					}
				}
			}
			return dist;
		}

		class Vertex implements Comparable<Vertex> {
			int  v;
			long dist;

			Vertex(int v, long dist)
			{
				this.v = v;
				this.dist = dist;
			}

			public int compareTo(Vertex o)
			{
				if(dist != o.dist)
				{
					return dist < o.dist ? -1 : 1;
				}
				return 0;
			}
		}

		class Edge {
			int dst;
			int length;

			Edge(int dst, int length)
			{
				this.dst = dst;
				this.length = length;
			}
		}
	}

	static @SuppressWarnings("ALL")
	class InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private BufferedInputStream din;
		private byte[]              buffer;
		private int                 bufferPointer;
		private int                 bytesRead;

		public InputReader(InputStream stream)
		{
			din = new BufferedInputStream(stream);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public InputReader(String file_name)
		{
			try
			{
				din = new BufferedInputStream(new FileInputStream(file_name));
			} catch(Exception e)
			{
				throw new InputMismatchException();
			}
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public int readInt()
		{
			int ret = 0;
			byte c = read();
			while(c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if(neg)
				c = read();
			do
			{
				ret = ret*10+c-'0';
			} while((c = read()) >= '0' && c <= '9');

			if(neg)
				return -ret;
			return ret;
		}

		private void fillBuffer()
		{
			try
			{
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			} catch(Exception e)
			{
				throw new InputMismatchException();
			}
			if(bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read()
		{
			if(bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}
	}

	static @SuppressWarnings("ALL")
	class ArrayUtils {
		public static void fill(int[] arr, int from, int to, int val)
		{
			int len = to-from+1;
			arr[from] = val;
			for(int i = 1; i < len; i += i)
				System.arraycopy(arr, from, arr, from+i, ((len-i) < i) ? (len-i) : i);
		}

		public static void fill(long[] arr, int from, int to, long val)
		{
			int len = to-from+1;
			arr[from] = val;
			for(int i = 1; i < len; i += i)
				System.arraycopy(arr, from, arr, from+i, ((len-i) < i) ? (len-i) : i);
		}

		public static <T> void fill(T[] arr, Supplier<T> fcn)
		{
//		Arrays.fill(arr, val);
			for(int i = 0; i < arr.length; i++)
				arr[i] = fcn.get();
		}

		public static <T> T[] array(int dim1, Supplier<T> fcn)
		{
			T[] ret = (T[]) Array.newInstance(fcn.get().getClass(), dim1);
			fill(ret, fcn);
			return (T[]) ret;
		}
	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream)
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void close()
		{
			writer.close();
		}

		public void printLine(long i)
		{
			writer.println(i);
		}
	}
}