Problem:
Score : 900 points

Problem Statement

You are given an undirected graph consisting of N vertices and M edges.
The vertices are numbered 1 to N, and the edges are numbered 1 to M.
In addition, each vertex has a label, A or B. The label of Vertex i is s_i.
Edge i bidirectionally connects vertex a_i and b_i.

The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.
Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.

For example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2, the resulting string is ABABB.

Determine if Nusook can make all strings consisting of A and B.

Constraints

2 \leq N \leq 2 \times 10^{5}

1 \leq M \leq 2 \times 10^{5}

|s| = N

s_i is A or B.

1 \leq a_i, b_i \leq N

The given graph may NOT be simple or connected.

Input

Input is given from Standard Input in the following format:

N M
s
a_1 b_1
:
a_{M} b_{M}

Output

If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.

Sample Input 1

2 3
AB
1 1
1 2
2 2

Sample Output 1

Yes

Since Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.

Sample Input 2

4 3
ABAB
1 2
2 3
3 1

Sample Output 2

No

For example, Nusook cannot make BB.

The given graph may not be connected.

Sample Input 3

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9

Sample Output 3

Yes

Sample Input 4

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11

Sample Output 4

No

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline

n,m = map(int,input().split())
s = input()
ab = [list(map(int, input().split(' '))) for i in range(m)]
graph = [[] for i in range(n+1)]
ABs = [[0,0] for i in range(n+1)]
for a,b in ab:
    graph[a].append(b)
    graph[b].append(a)
    if s[a-1] == "A":
        ABs[b][0] += 1
    else:
        ABs[b][1] += 1
    if s[b-1] == "A":
        ABs[a][0] += 1
    else:
        ABs[a][1] += 1
ablack = [-1 for i in range(n+1)]
ablack[0] = 0
for x in range(1,n+1):
    if ABs[x][0] == 0 or ABs[x][1] == 0:
        if s[x-1] == "A":
            ablack[x] = 0
        else:
            ablack[x] = 1
stack = []
visited = [0 for i in range(n+1)]
for i in range(1,n+1):
    if ablack[i] >= 0:
        stack.append(i)
while stack:
    x = stack.pop()
    visited[x] = 1
    for y in graph[x]:
        if visited[y] == 0:
            if ablack[x] == 0:
                ABs[y][0] -= 1
            else:
                ABs[y][1] -= 1
            if ABs[y][0] <= 0 or ABs[y][1] <= 0:
                if s[y-1] == "A":
                    ablack[y] = 0
                else:
                    ablack[y] = 1
                stack.append(y)
if ablack.count(-1) >= 2:
    print("Yes")
else:
    print("No")