A10034 | Fibonotci

Fibonotci sequence is an integer recursive sequence defined by the recurrence relation

$F_{n}=s_{n-1}·F_{n-1}+s_{n-2}·F_{n-2}$ with $F_{0}=0,F_{1}=1$ 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:

s = (5,3,8,11,5,3,7,11,5,3,8,11,…) 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 .

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 should contain a single integer equal to .