Problem: There is a string S of length N consisting of characters `0` and `1`. You will perform the following operation for each i = 1, 2, ..., m:

* Arbitrarily permute the characters within the substring of S starting at the l_i-th character from the left and extending through the r_i-th character.



Here, the sequence l_i is non-decreasing.

How many values are possible for S after the M operations, modulo 1000000007(= 10^9+7)?

Constraints

* 2≦N≦3000
* 1≦M≦3000
* S consists of characters `0` and `1`.
* The length of S equals N.
* 1≦l_i < r_i≦N
* l_i ≦ l_{i+1}

Input

The input is given from Standard Input in the following format:


N M
S
l_1 r_1
:
l_M r_M


Output

Print the number of the possible values for S after the M operations, modulo 1000000007.

Examples

Input

5 2
01001
2 4
3 5


Output

6


Input

9 3
110111110
1 4
4 6
6 9


Output

26


Input

11 6
00101000110
2 4
2 3
4 7
5 6
6 10
10 11


Output

143

Solution (in PYTHON3):

Solution:
mod=10**9+7

N,M=map(int,input().split())
L=-1;R=-1
S=input()
ope=[]
for i in range(M):
    l,r=map(int,input().split())
    l-=1;r-=1
    if L<=l and r<=R:
        continue
    else:
        L,R=l,r
        ope.append((l,r))

M=len(ope)
data=[-1]*N
for i in range(M):
    l,r=ope[i]
    for j in range(l,r+1):
        data[j]=i

dp=[[0 for i in range(N+1)] for j in range(N+1)]

for j in range(N+1):
    dp[-1][j]=1

for i in range(N-1,-1,-1):
    id=data[i]
    if id!=-1:
        l,r=ope[id]
        temp1=sum(int(S[k]) for k in range(r+1))
        temp0=r+1-temp1
        for j in range(temp1+1):
            np1=temp1-j
            np0=temp0-(i-j)
            if np1==0:
                if np0>0:
                    dp[i][j]=dp[i+1][j]
            else:
                if np0>0:
                    dp[i][j]=(dp[i+1][j+1]+dp[i+1][j])%mod
                elif np0==0:
                    dp[i][j]=dp[i+1][j+1]
    else:
        if S[i]=="1":
            for j in range(N):
                dp[i][j]=dp[i+1][j+1]
        else:
            for j in range(N+1):
                dp[i][j]=dp[i+1][j]

print(dp[0][0])