Codeforces Round #475 (Div. 2) C. Alternating Sum（等比數列+逆元）

C. Alternating Sum time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

You are given two integers aa and bb. Moreover, you are given a sequence s0,s1,…,sns0,s1,…,sn. All values in ss are integers 11 or −1−1. It's known that sequence is kk-periodic and kk divides n+1n+1. In other words, for each k≤i≤nk≤i≤n it's satisfied that si=si−ksi=si−k.

Find out the non-negative remainder of division of n∑i=0sian−ibi∑i=0nsian−ibi by 109+9109+9.

Note that the modulo is unusual! Input

The first line contains four integers n,a,bn,a,b and kk (1≤n≤109,1≤a,b≤109,1≤k≤105)(1≤n≤109,1≤a,b≤109,1≤k≤105).

The second line contains a sequence of length kk consisting of characters '+' and '-'.

If the ii-th character (0-indexed) is '+', then s