### Shuffling

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.

```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`.

```9 3
110111110
1 4
4 6
6 9
```

```26
```

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

```143
```

### Submitting .cpp to 'Shuffling'

Time Limit: 2 Seconds
Memory Limit: 1024MB
No. of ACs: 12