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.*;
import java.lang.reflect.Array;
import java.util.*;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.stream.Collectors;

@SuppressWarnings("unused")
public class Main {
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	final int MOD = (int)1e9+7;
	
	//System.out.println();はつかわない！！
	void solve() throws Exception{
		int N = in.nextInt(), M = in.nextInt();
		ArrayList<ArrayList<Integer>> G = new ArrayList<>();
		for(int i = 0; i < N; i++) G.add(new ArrayList<>());
		for(int i = 0; i < M; i++){
			int u = in.nextInt()-1, v = in.nextInt()-1;
			G.get(u).add(v);
		}
		int s = in.nextInt()-1, t = in.nextInt()-1;
		
		long[][] dist = new long[3][N];
		for(int i = 0; i < 3; i++) Arrays.fill(dist[i], Long.MAX_VALUE / 2);
		Queue<List<Integer>> queue = new ArrayDeque<List<Integer>>();
		queue.add(Arrays.asList(s, 0));
		dist[0][s] = 0;
		
		while(!queue.isEmpty()){
			List<Integer> e = queue.poll();
			int v = e.get(0), m = e.get(1);
			for(int next : G.get(v)){
				if(dist[(m+1)%3][next] > dist[m][v] + 1){
					dist[(m+1)%3][next] = dist[m][v] + 1;
					queue.add(Arrays.asList(next, (m+1)%3));
				}
			}
		}
		
		out.println(dist[0][t] == Long.MAX_VALUE / 2 ? -1 : dist[0][t] / 3);
	}
	
	
	
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		solve();
		out.flush();
	}
	
	class FastScanner {
		Reader input;

		FastScanner() {this(System.in);}
		FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}
		
		int nextInt() {return (int) nextLong();}

		long nextLong() {
			try {
				int sign = 1;
				int b = input.read();
				while ((b < '0' || '9' < b) && b != '-' && b != '+') {
					b = input.read();
				}
				if (b == '-') {
					sign = -1;
					b = input.read();
				} else if (b == '+') {
					b = input.read();
				}
				long ret = b - '0';
				while (true) {
					b = input.read();
					if (b < '0' || '9' < b) return ret * sign;
					ret *= 10;
					ret += b - '0';
				}
			} catch (IOException e) {
				e.printStackTrace();
				return -1;
			}
		}

		double nextDouble() {
			try {
				double sign = 1;
				int b = input.read();
				while ((b < '0' || '9' < b) && b != '-' && b != '+') {
					b = input.read();
				}
				if (b == '-') {
					sign = -1;
					b = input.read();
				} else if (b == '+') {
					b = input.read();
				}
				double ret = b - '0';
				while (true) {
					b = input.read();
					if (b < '0' || '9' < b) break;
					ret *= 10;
					ret += b - '0';
				}
				if (b != '.') return sign * ret;
				double div = 1;
				b = input.read();
				while ('0' <= b && b <= '9') {
					ret *= 10;
					ret += b - '0';
					div *= 10;
					b = input.read();
				}
				return sign * ret / div;
			} catch (IOException e) {
				e.printStackTrace();
				return Double.NaN;
			}
		}

		char nextChar() {
			try {
				int b = input.read();
				while (Character.isWhitespace(b)) {
					b = input.read();
				}
				return (char) b;
			} catch (IOException e) {
				e.printStackTrace();
				return 0;
			}
		}

		String nextStr() {
			try {
				StringBuilder sb = new StringBuilder();
				int b = input.read();
				while (Character.isWhitespace(b)) {
					b = input.read();
				}
				while (b != -1 && !Character.isWhitespace(b)) {
					sb.append((char) b);
					b = input.read();
				}
				return sb.toString();
			} catch (IOException e) {
				e.printStackTrace();
				return "";
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}
 
		public int[] nextIntArrayDec(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}
 
		public int[] nextIntArray1Index(int n) {
			int[] res = new int[n + 1];
			for (int i = 0; i < n; i++) {
				res[i + 1] = nextInt();
			}
			return res;
		}
 
		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}
 
		public long[] nextLongArrayDec(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}
 
		public long[] nextLongArray1Index(int n) {
			long[] res = new long[n + 1];
			for (int i = 0; i < n; i++) {
				res[i + 1] = nextLong();
			}
			return res;
		}
 
		public double[] nextDoubleArray(int n) {
			double[] res = new double[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}
	}
}

class CombCalculator{
	//引数の最大値、MOD、階乗・MODの逆元・階乗の逆元のテーブル
	static int MAX_FAC = 510000;
	static int MOD = (int)1e9+7;
	static long[] fac = new long[MAX_FAC+1];
	static long[] finv = new long[MAX_FAC+1];
	static long[] inv = new long[MAX_FAC+1];
	
	public CombCalculator(){
		this(510000, (int)1e9+7);
	}
	
	public CombCalculator(int max, int mod){
		MAX_FAC = max; MOD = mod;
		initComb();
	}
	
	//テーブルの初期化
	void initComb(){
		fac[0] = finv[0] = inv[0] = fac[1] = finv[1] = inv[1] = 1;
		for (int i = 2; i <= MAX_FAC; ++i) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - (MOD / i) * inv[(int) (MOD % i)] % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
	}
	
	//nPk % MOD
	public long modPerm(int n, int k){
		return fac[n] * finv[n - k] % MOD;
	}
	
	//nCk % MOD
	public long modComb(int n, int k){
		return fac[n] * finv[k] % MOD * finv[n - k] % MOD;
	}
	
	//n! % MOD
	public long modFact(int n){
		return fac[n];
	}
	
	//(n!)^-1 % MOD
	public long modFactInv(int n){
		return finv[n];
	}
	
	//n^-1 % MOD
	public long modInv(int n){
		return inv[n];
	}
	
	/*
	 * MOD付きpowをlog(n)で計算
	 */
	static long modPow(long a, long n, int mod){
		long res = 1;
		while(n > 0){
			if((n & 1) == 1) res = (res * a) % mod;
			a = (a * a) % mod;
			n = n >> 1;
		}
		return res;
	}
}
/* end Main */