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 CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int MAXN=3005;
const int MOD=1e9+7;

int n,m;
int d[MAXN][MAXN],right[MAXN],sum[MAXN];
char s[MAXN];

int main(){
    scanf("%d%d%s",&n,&m,s+1);
    for(int i=1;i<=n;i++) sum[i]=s[i]-'0';
    for(int i=1;i<=n+1;i++) sum[i]+=sum[i-1];
    for(int i=1;i<=n+1;i++) right[i]=i;
    for(int i=1;i<=m;i++){
        int l,r;
        scanf("%d%d",&l,&r);
        right[l]=max(right[l],r);
    }
    for(int i=1;i<=n;i++)
        right[i]=max(right[i],right[i-1]);
    d[1][sum[right[1]]]=1;
    for(int i=1;i<=n;i++)
        for(int j=0;j<=n;j++){
            if(d[i][j]){
                int l=right[i]+1,r=right[i+1];
                int x=j,y=right[i]-i+1-j;
                if(x) (d[i+1][j-1+sum[r]-sum[l-1]]+=d[i][j])%=MOD;
                if(y) (d[i+1][j+sum[r]-sum[l-1]]+=d[i][j])%=MOD;
            }
        }
    printf("%d\n",(d[n+1][0]+MOD)%MOD);
}