Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

2

Ken can reach Vertex 3 from Vertex 1 in two ken-ken-pa, as follows: 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 in the first ken-ken-pa, then 4 \rightarrow 1 \rightarrow 2 \rightarrow 3 in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.

Sample Input 2

3 3
1 2
2 3
3 1
1 2

Sample Output 2

-1

Any number of ken-ken-pa will bring Ken back to Vertex 1, so he cannot reach Vertex 2, though he can pass through it in the middle of a ken-ken-pa.

Sample Input 3

2 0
1 2

Sample Output 3

-1

Vertex S and Vertex T may be disconnected.

Sample Input 4

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

Sample Output 4

2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;

public class Main {
	
	ArrayList<HashSet<Integer>> edgeList;
	ArrayList<HashSet<Integer>> threeStepEdgeList;

	public static void main(String[] args) throws IOException {
		Main mainObj = new Main();
		mainObj.solve();
	}

	public void solve() throws IOException {
		FastScanner fs = new FastScanner();
		int n = fs.nextInt();
		int m = fs.nextInt();
		
		edgeList = new ArrayList<>(n);
		threeStepEdgeList = new ArrayList<>(n);
		for(int i = 0; i < n; i++) {
			edgeList.add(new HashSet<>());
			threeStepEdgeList.add(new HashSet<>());
		}
		
		for(int i = 0; i< m; i++) {
			int from = fs.nextInt()-1;
			int to = fs.nextInt()-1;
			edgeList.get(from).add(to);
		}
		
		for(int i = 0; i < n; i++) {
			dfs(1, i, i);
		}
		
		int start = fs.nextInt()-1;
		int end = fs.nextInt()-1;
		
		int[] visitedNode = new int[n];
		ArrayDeque<Node> queue = new ArrayDeque<>();
		queue.add(new Node(start, 0));
		visitedNode[start] = 1;
		
		while(!queue.isEmpty()) {
			Node thisNode = queue.poll();
			
			if(thisNode.id == end) {
				System.out.println(thisNode.depth);
				return;
			}
			
			for(Integer nextNode : threeStepEdgeList.get(thisNode.id)) {
				if(visitedNode[nextNode] == 1) {
					continue;
				}
				
				queue.add(new Node(nextNode, thisNode.depth+1));
				visitedNode[nextNode] = 1;
			}
		}
		
		System.out.println(-1);
	}
	
	class Node{
		int depth;
		int id;
		Node(int id, int depth){
			this.id = id;
			this.depth = depth;
		}
	}
	
	void dfs(int depth, int nowEdge, int start) {
		if(depth == 3) {
			threeStepEdgeList.get(start).add(nowEdge);
			return;
		}
		
		for(Integer nextEdge : edgeList.get(nowEdge)) {
			dfs(depth+1, nextEdge, start);
		}
	}
	
	public class FastScanner {

		BufferedReader reader;
		private StringTokenizer st;

		public FastScanner() {
			st = null;
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements()) {
				st = new StringTokenizer(reader.readLine());
			}
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			st = null;
			String readLine = null;
			readLine = reader.readLine();
			return readLine;
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		public int[] nextIntArr(int n) throws NumberFormatException, IOException {
			int[] retArr = new int[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextInt();
			}
			return retArr;
		}

		public long[] nextLongArr(int n) throws NumberFormatException, IOException {
			long[] retArr = new long[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextLong();
			}
			return retArr;
		}

		public void close() throws IOException {
			reader.close();
		}
	}

}