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;
using Int = long long;

template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n,q;
  string s;
  cin>>n>>q>>s;
  vector<Int> v(n);
  for(Int i=0;i<n;i++) v[i]=i+1;
  for(Int i=0;i<q;i++){
    Int l,r;
    cin>>l>>r;
    l--;
    chmax(v[l],r);
  }
  for(Int i=1;i<n;i++) chmax(v[i],v[i-1]);
  vector<Int> c(n+1,0);
  for(Int i=0;i<n;i++) c[i+1]=c[i]+(s[i]=='1');

  const Int MOD = 1e9+7;
  vector<Int> dp(n+1,0);
  dp[0]=1;
  for(Int i=0;i<n;i++){
    vector<Int> nx(n+1,0);
    for(Int j=0;j<=n;j++){
      //cout<<i<<" "<<j<<":"<<dp[j]<<endl;
      if(j<c[v[i]]) nx[j+1]+=dp[j];
      if(i-j<v[i]-c[v[i]]) nx[j]+=dp[j];
      nx[j]%=MOD;
    }
    swap(dp,nx);
  }
  cout<<dp[c[n]]<<endl;
  return 0;
}