Codeforces Round #475 (Div. 2) C. Alternating Sum (geometric series + inverse)

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

You are given the integers AA and BB. Moreover, given a sequence s0,s1,..., sns0,s1,..., sn. All values in SS is integers one or−1−1. It ' s known that sequence is kk-periodic and KK divides n+1n+1. In the 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 ' + ' and then s