Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

5 2
01001
2 4
3 5

Sample Output 1

6

After the first operation, S can be one of the following three: 01001, 00101 and 00011.

After the second operation, S can be one of the following six: 01100, 01010, 01001, 00011, 00101 and 00110.

Sample Input 2

9 3
110111110
1 4
4 6
6 9

Sample Output 2

26

Sample Input 3

11 6
00101000110
2 4
2 3
4 7
5 6
6 10
10 11

Sample Output 3

143

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
const int MAXN=3000;
const int MOD=1e9+7;
void A(int& a,int b){a+=b;if(a>=MOD)a-=MOD;}
int n,m,r[MAXN+10],f[MAXN+10][MAXN+10],sm[MAXN+10];
char s[MAXN+10];
int main()
{
	scanf("%d%d%s",&n,&m,s+1);
	for(int i=1;i<=n;++i)sm[i]=sm[i-1]+s[i]-'0',r[i]=i;
	for(int i=1,a,b;i<=m;++i)
	{
		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]);
	f[1][sm[r[1]]]=1;
	for(int i=1;i<n;++i)
	{
		for(int j=0;j<=n;++j)
		{
			if(f[i][j]==0)continue;
			int k=sm[r[i+1]]-sm[r[i]];
			if((r[i]>i||s[i]=='0')&&j<r[i]-i+1&&j+k<=r[i+1]-i)A(f[i+1][j+k],f[i][j]);
			if((r[i]>i||s[i]=='1')&&j>0&&j+k-1<=r[i+1]-i)A(f[i+1][j+k-1],f[i][j]);
		}
	}
	int ans=0;A(ans,f[n][0]);A(ans,f[n][1]);
	printf("%d",ans);
	return 0;
}