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 <bits/stdc++.h>
        using namespace std;
   #define int long long
    const int MAX =200002;
const int MOD =1000000007;

     signed main(){
int n,m;
cin>>n>>m;
string s;
cin>>s;
int x[n+1];
for(int i=0;i<=n;i++)x[i]=i;
int l,r;
for(int i=0;i<m;i++){
    cin>>l>>r;
    x[l]=max(x[l],r);
}
for(int i=0;i<n;i++)x[i+1]=max(x[i],x[i+1]);
map<pair<int,int>,int> mp1,mp2;
mp1[{0,0}]=1;

for(int i=0;i<n;i++){
    int t0=0,t1=0;
    for(int j=x[i];j<x[i+1];j++){
        if(s[j]=='0')t0++;
        else t1++;
    }
    for(auto&& j:mp1){
        pair<int,int>p={j.first.first+t0,j.first.second+t1};
        if(p.first!=0)mp2[{p.first-1,p.second}]=(mp2[{p.first-1,p.second}]+j.second)%MOD;
        if(p.second!=0)mp2[{p.first,p.second-1}]=(mp2[{p.first,p.second-1}]+j.second)%MOD;
    }
    swap(mp1,mp2);
    mp2.clear();
   
}
  
cout<<mp1[{0,0}]<<endl;

     }