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:
import sys
readline = sys.stdin.readline

MOD = 10**9+7
N, M = map(int, readline().split())
S = list(map(int, readline().strip()))
Query = [tuple(map(lambda x: int(x) - 1, readline().split())) for _ in range(M)]

PP = S.count(1)

Li = [None]*PP
Ri = [None]*PP

T1 = S[:]
for l, r in Query:
    cnt = 0
    for i in range(l, r+1):
        cnt += T1[i]
    for i in range(l, l+cnt):
        T1[i] = 1
    for i in range(l+cnt, r+1):
        T1[i] = 0
T2 = S[:]
for l, r in Query:
    cnt = 0
    for i in range(l, r+1):
        cnt += 1 - T2[i]
    for i in range(l, l+cnt):
        T2[i] = 0
    for i in range(l+cnt, r+1):
        T2[i] = 1

cnt = 0
for i in range(N):
    if T1[i]:
        Li[cnt] = i
        cnt += 1
cnt = 0
for i in range(N):
    if T2[i]:
        Ri[cnt] = i+1
        cnt += 1

dp = [0]*N
for i in range(Li[0], Ri[0]):
    dp[i] = 1

for j in range(1, PP):
    dp2 = [0] + dp[:-1]
    for i in range(1, N):
        dp2[i] = (dp2[i]+dp2[i-1])%MOD
    for i in range(Li[j]):
        dp2[i] = 0
    for i in range(Ri[j], N):
        dp2[i] = 0
    dp = dp2[:]
res = 0
for d in dp:
    res = (res+d)%MOD
print(res)