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>
#include<map>
using namespace std;
typedef long long ll;
const int N=3005;
const int mod=1e9+7;
char str[N];
int r[N];
int d[N][N];
int s[N];
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    scanf("%s",str+1);
    for(int i=1;i<=n;i++){
        s[i]=str[i]-'0';
    }
    for(int i=1;i<=n+1;i++)
        s[i]+=s[i-1];
    for(int i=1;i<=n+1;i++)
        r[i]=i;
    for(int i=1;i<=m;i++){
        int a,b;
        scanf("%d%d",&a,&b);
        r[a]=max(r[a],b);
    }
    for(int i=1;i<=n;i++)
        r[i]=max(r[i],r[i-1]);
    d[1][s[r[1]]]=1;
    for(int i=1;i<=n;i++)
        for(int j=0;j<=n;j++)
            if(d[i][j]){
                int a=r[i],b=r[i+1];
                int f=s[b]-s[a];
                if(j){
                    d[i+1][j+f-1]+=d[i][j];
                    d[i+1][j+f-1]%=mod;
                }
                if(r[i]!=i+j-1){
                    d[i+1][j+f]+=d[i][j];
                    d[i+1][j+f]%=mod;
                }
            }
    int ans=d[n+1][0];
    printf("%d\n",ans);
}