## DMOPC '19 Contest 6 P3 - Grade 11 Math

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Points: 10 (partial)
Time limit: 2.0s
Memory limit: 256M

Author:
Problem types

Serena is learning about binary numbers in math class! She is given a binary number , and she is also given series of operations which she must perform on it. In one operation, she sets all bits in the 1-indexed range to , and outputs the base-10 value of the binary number, modulo .

The base-10 value of a binary number of length consisting of digits and is given by the sum of over all in .

#### Input Specification

The first line contains two space-separated integers, and , the length of the number and the number of operations.
The next line contains , the original binary number.
The next lines contain two space-separated integers, and , representing an operation described in the problem statement.

#### Output Specification

For each operation, output the base-10 value of the binary number after performing the operation, modulo .

#### Constraints

In all subtasks,

##### Subtask 2 [80%]

No additional constraints.

#### Sample Input 1

5 2
01000
1 3
2 4

#### Sample Output 1

28
30

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