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 <cstdio>
#include <cstring>
#include <algorithm>
#define R register
using namespace std;
const int mod=1000000007;
const int MAXN=3100;
int pre[MAXN];
int dp[MAXN][MAXN],r[MAXN];
char s[MAXN];

void reads(char* st)
{
	int len=0;char ch=getchar();
	while(ch<'0'||ch>'1')ch=getchar();
	while(ch>='0'&&ch<='1')st[++len]=ch,ch=getchar();
}

void add(int &x,int y)
{x=(x+y)%mod;}

int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	reads(s);
	for(int i=1;i<=n;++i)
	  if(s[i]=='1')pre[i]=pre[i-1]+1;
	  else pre[i]=pre[i-1];
	pre[n+1]=pre[n];
	int t1,t2;
	for(R int i=1;i<=n+1;++i)r[i]=i;
	for(R int i=1;i<=m;++i)
	{
		scanf("%d%d",&t1,&t2);
		if(t2>r[t1])r[t1]=t2;
	}
	for(R int i=1;i<=n+1;++i)
	  if(r[i-1]>r[i])r[i]=r[i-1];
	dp[1][pre[r[1]]]=1;
	for(R int i=1;i<=n;++i)
	  for(R int j=0;j<=n;++j)
	    if(dp[i][j])
	    {
	    	if(r[i]-i-j+1)add(dp[i+1][j+pre[r[i+1]]-pre[r[i]]],dp[i][j]);
	    	if(j)add(dp[i+1][j-1+pre[r[i+1]]-pre[r[i]]],dp[i][j]);
	    }
	printf("%d\n",dp[n+1][0]);
	return 0;
}