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.

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

inputFormat

Input

The input is given from Standard Input in the following format:

N M S l_1 r_1 : l_M r_M

outputFormat

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

样例

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

143