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data structures

math

matrices

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A. Fibonotci

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFibonotci sequence is an integer recursive sequence defined by the recurrence relation

Sequence *s* is an infinite and almost cyclic sequence with a cycle of length *N*. A sequence *s* is called almost cyclic with a cycle of length *N* if , for *i* ≥ *N*, except for a finite number of values *s*_{i}, for which (*i* ≥ *N*).

Following is an example of an almost cyclic sequence with a cycle of length 4:

Notice that the only value of *s* for which the equality does not hold is *s*_{6} (*s*_{6} = 7 and *s*_{2} = 8). You are given *s*_{0}, *s*_{1}, ...*s*_{N - 1} and all the values of sequence *s* for which (*i* ≥ *N*).

Find .

Input

The first line contains two numbers *K* and *P*. The second line contains a single number *N*. The third line contains *N* numbers separated by spaces, that represent the first *N* numbers of the sequence *s*. The fourth line contains a single number *M*, the number of values of sequence *s* for which . Each of the following *M* lines contains two numbers *j* and *v*, indicating that and *s*_{j} = *v*. All j-s are distinct.

- 1 ≤
*N*,*M*≤ 50000 - 0 ≤
*K*≤ 10^{18} - 1 ≤
*P*≤ 10^{9} - 1 ≤
*s*_{i}≤ 10^{9}, for all*i*= 0, 1, ...*N*- 1 -
*N*≤*j*≤ 10^{18} - 1 ≤
*v*≤ 10^{9} - All values are integers

Output

Output should contain a single integer equal to .

Examples

Input

10 8

3

1 2 1

2

7 3

5 4

Output

4

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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