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
N, M = map(int, input().split())

to = [[] for _ in range(N)]
dist = [[0 for _ in range(3)] for _ in range(100005)]
for i in range(M):
  a, b = map(int, input().split())
  a -= 1
  b -= 1
  to[a].append(b)

sv, tv = map(int, input().split())
sv -= 1
tv -= 1

for i in range(N):
  for j in range(3):
    dist[i][j] = float("inf")
q = [[sv, 0]]
dist[sv][0] = 0
while len(q) != 0:
  v = q[0][0]
  l = q[0][1]
  q.pop(0)
  for u in to[v]:
    nl = (l + 1) % 3
    if dist[u][nl] != float("inf"):
      continue
    dist[u][nl] = dist[v][l] + 1
    q.append([u, nl])
ans = dist[tv][0]
if ans == float("inf"):
  ans = -1
else:
  ans //= 3
print(ans)