Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G. G consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.

First, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.

Determine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.

Constraints

* 2 \leq N \leq 10^5
* 0 \leq M \leq \min(10^5, N (N-1))
* 1 \leq u_i, v_i \leq N(1 \leq i \leq M)
* u_i \neq v_i (1 \leq i \leq M)
* If i \neq j, (u_i, v_i) \neq (u_j, v_j).
* 1 \leq S, T \leq N
* S \neq T

Input

Input is given from Standard Input in the following format:


N M
u_1 v_1
:
u_M v_M
S T


Output

If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1. If he can, print the minimum number of ken-ken-pa needed to reach vertex T.

Examples

Input

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


Output

2


Input

3 3
1 2
2 3
3 1
1 2


Output

-1


Input

2 0
1 2


Output

-1


Input

6 8
1 2
2 3
3 4
4 5
5 1
1 4
1 5
4 6
1 6


Output

2
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Queue;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		int m = Integer.parseInt(sa[1]);
		Map<Integer, List<Integer>> map = new HashMap<>();
		for (int i = 0; i < m; i++) {
			sa = br.readLine().split(" ");
			int u = Integer.parseInt(sa[0]) - 1;
			int v = Integer.parseInt(sa[1]) - 1;
			List<Integer> list = map.get(u);
			if (list == null) {
				list = new ArrayList<>();
				map.put(u, list);
			}
			list.add(v);
		}
		sa = br.readLine().split(" ");
		int s = Integer.parseInt(sa[0]) - 1;
		int t = Integer.parseInt(sa[1]) - 1;
		br.close();

		boolean[][] visit = new boolean[n][3];
		int[] cnt = new int[n];
		visit[s][0] = true;
		cnt[s] = 1;
		Queue<Ken> que = new ArrayDeque<Ken>();
		Ken ken = new Ken();
		ken.p = s;
		ken.cnt = 1;
		que.add(ken);
		while (!que.isEmpty()) {
			Ken cur = que.poll();
			List<Integer> list = map.get(cur.p);
			if (list == null) {
				continue;
			}
			for (int next : list) {
				if (cur.k == 2) {
					if (!visit[next][0]) {
						visit[next][0] = true;
						cnt[next] = cur.cnt + 1;
						if (next == t) {
							break;
						}
						ken = new Ken();
						ken.p = next;
						ken.cnt = cnt[next];
						que.add(ken);
					}
				} else {
					if (!visit[next][cur.k + 1]) {
						visit[next][cur.k + 1] = true;
						ken = new Ken();
						ken.p = next;
						ken.k = cur.k + 1;
						ken.cnt = cur.cnt;
						que.add(ken);
					}
				}
			}
		}
		System.out.println(cnt[t] - 1);
	}

	static class Ken {
		int p, k, cnt;
	}
}
