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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
const int N=3010,Mo=1000000007;
int n,m;
char s[N];
int f[N][N],w[N],r[N],id[N];
inline int gi() {
    int x=0,o=1;
    char ch=getchar();
    while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
    if(ch=='-') o=-1,ch=getchar();
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*o;
}
int main() {
    cin>>n>>m;
    scanf("%s",s+1);
    for(int i=1;i<=n;i++) w[i]=w[i-1]+s[i]-'0',r[i]=i;
    for(int i=1;i<=m;i++) {
	int x=gi(),y=gi();
	for(int j=x;j<=y;j++) r[j]=max(r[j],y);
    }
    f[0][0]=1;
    for(int i=1;i<=n;i++)
	for(int j=max(0,i-r[i]+w[r[i]]);j<=w[r[i]];j++)
	    f[i][j]=(f[i-1][j]+f[i-1][j-1])%Mo;
    cout<<f[n][w[n]];
    return 0;
}