#include<cstdio>
#include<algorithm>
using namespace std;
inline int read()
{
	int x;char c;
	while((c=getchar())<'0'||c>'9');
	for(x=c-'0';(c=getchar())>='0'&&c<='9';)x=x*10+c-'0';
	return x;
}
#define MN 3000
#define MOD 1000000007
char S[MN+5];
int s[MN+5],l[MN+5],r[MN+5],f[MN+5][MN+5];
inline void rw(int&a,int b){if((a+=b)>=MOD)a-=MOD;}
int main()
{
	int n,m,i,j,k;
	n=read();m=read();
	scanf("%s",S+1);
	for(i=1;i<=n;++i)s[i]=s[i-1]+(S[i]=='1');
	for(i=1;i<=m;++i)
	{
		l[i]=read();r[i]=read();
		if(l[i]==l[i-1])r[i-1]=max(r[i-1],r[i]);
		if(r[i]<=r[i-1]){--i;--m;continue;}
	}
	l[i]=r[i]=n+2;f[0][0]=1;
	for(i=j=0;i<=n;++i)
	{
		if(i==l[j+1])++j;
		for(k=0;k<=n;++k)if(f[i][k])
		{
			if(i+1<l[j+1])
			{
				if(i>r[j]||k<=r[j]-i)rw(f[i+1][k],f[i][k]);
				if(k)rw(f[i+1][k-1],f[i][k]);
			}
			else
			{
				if(i>r[j])rw(f[i+1][k+s[r[j+1]]-s[i]],f[i][k]);
				else if(k<=r[j]-i)rw(f[i+1][k+s[r[j+1]]-s[r[j]]],f[i][k]);
				if(k)rw(f[i+1][k-1+s[r[j+1]]-s[r[j]]],f[i][k]);
			}
		}
	}
	printf("%d",f[n+1][0]);
}
### Prompt

Develop a solution in Cpp to the problem described below:

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

### Response

```cpp
#include<cstdio>
#include<algorithm>
using namespace std;
inline int read()
{
	int x;char c;
	while((c=getchar())<'0'||c>'9');
	for(x=c-'0';(c=getchar())>='0'&&c<='9';)x=x*10+c-'0';
	return x;
}
#define MN 3000
#define MOD 1000000007
char S[MN+5];
int s[MN+5],l[MN+5],r[MN+5],f[MN+5][MN+5];
inline void rw(int&a,int b){if((a+=b)>=MOD)a-=MOD;}
int main()
{
	int n,m,i,j,k;
	n=read();m=read();
	scanf("%s",S+1);
	for(i=1;i<=n;++i)s[i]=s[i-1]+(S[i]=='1');
	for(i=1;i<=m;++i)
	{
		l[i]=read();r[i]=read();
		if(l[i]==l[i-1])r[i-1]=max(r[i-1],r[i]);
		if(r[i]<=r[i-1]){--i;--m;continue;}
	}
	l[i]=r[i]=n+2;f[0][0]=1;
	for(i=j=0;i<=n;++i)
	{
		if(i==l[j+1])++j;
		for(k=0;k<=n;++k)if(f[i][k])
		{
			if(i+1<l[j+1])
			{
				if(i>r[j]||k<=r[j]-i)rw(f[i+1][k],f[i][k]);
				if(k)rw(f[i+1][k-1],f[i][k]);
			}
			else
			{
				if(i>r[j])rw(f[i+1][k+s[r[j+1]]-s[i]],f[i][k]);
				else if(k<=r[j]-i)rw(f[i+1][k+s[r[j+1]]-s[r[j]]],f[i][k]);
				if(k)rw(f[i+1][k-1+s[r[j+1]]-s[r[j]]],f[i][k]);
			}
		}
	}
	printf("%d",f[n+1][0]);
}
```