#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000009;
long long powe(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) (res *= a) %= MOD;
    b >>= 1;
    a = (a * a) % MOD;
  }
  return res;
}
long long inv(int a) { return powe(a, MOD - 2); }
char S[111111];
int main() {
  int N, A, B, K;
  scanf("%d%d%d%d%s", &N, &A, &B, &K, S);
  long long result = 0;
  for (int i = 0; i < (K); ++i) {
    result +=
        ((S[i] == '+' ? 1 : -1) * powe(A, N - i) % MOD) * powe(B, i) % MOD;
    result %= MOD;
  }
  int L = (N + 1) / K;
  long long X = powe(B, K) * inv(powe(A, K)) % MOD;
  if (X == 1) {
    result *= L;
  } else {
    result *= (powe(X, L) - 1) * inv(X - 1) % MOD;
  }
  result %= MOD;
  result += MOD;
  result %= MOD;
  printf("%d\n", (int)result);
}

### Prompt

Generate a Cpp solution to the following problem:

You are given two integers a and b. Moreover, you are given a sequence s_0, s_1, ..., s_{n}. All values in s are integers 1 or -1. It's known that sequence is k-periodic and k divides n+1. In other words, for each k ≤ i ≤ n it's satisfied that s_{i} = s_{i - k}.

Find out the non-negative remainder of division of ∑ _{i=0}^{n} s_{i} a^{n - i} b^{i} by 10^{9} + 9.

Note that the modulo is unusual!

Input

The first line contains four integers n, a, b and k (1 ≤ n ≤ 10^{9}, 1 ≤ a, b ≤ 10^{9}, 1 ≤ k ≤ 10^{5}).

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

If the i-th character (0-indexed) is '+', then s_{i} = 1, otherwise s_{i} = -1.

Note that only the first k members of the sequence are given, the rest can be obtained using the periodicity property.

Output

Output a single integer — value of given expression modulo 10^{9} + 9.

Examples

Input

2 2 3 3
+-+


Output

7


Input

4 1 5 1
-


Output

999999228

Note

In the first example:

(∑ _{i=0}^{n} s_{i} a^{n - i} b^{i}) = 2^{2} 3^{0} - 2^{1} 3^{1} + 2^{0} 3^{2} = 7

In the second example:

(∑ _{i=0}^{n} s_{i} a^{n - i} b^{i}) = -1^{4} 5^{0} - 1^{3} 5^{1} - 1^{2} 5^{2} - 1^{1} 5^{3} - 1^{0} 5^{4} = -781 ≡ 999999228 \pmod{10^{9} + 9}.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000009;
long long powe(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) (res *= a) %= MOD;
    b >>= 1;
    a = (a * a) % MOD;
  }
  return res;
}
long long inv(int a) { return powe(a, MOD - 2); }
char S[111111];
int main() {
  int N, A, B, K;
  scanf("%d%d%d%d%s", &N, &A, &B, &K, S);
  long long result = 0;
  for (int i = 0; i < (K); ++i) {
    result +=
        ((S[i] == '+' ? 1 : -1) * powe(A, N - i) % MOD) * powe(B, i) % MOD;
    result %= MOD;
  }
  int L = (N + 1) / K;
  long long X = powe(B, K) * inv(powe(A, K)) % MOD;
  if (X == 1) {
    result *= L;
  } else {
    result *= (powe(X, L) - 1) * inv(X - 1) % MOD;
  }
  result %= MOD;
  result += MOD;
  result %= MOD;
  printf("%d\n", (int)result);
}

```