#include <bits/stdc++.h>
using namespace std;
const int K = 1e5 + 7, M = 1e9 + 9;
int fp(int x, int y) {
  int ret = 1;
  for (; y; y >>= 1, x = (long long)x * x % M)
    if (y & 1) ret = (long long)ret * x % M;
  return ret;
}
int n, a, b, k;
char s[K];
int main() {
  scanf("%d%d%d%d", &n, &a, &b, &k);
  scanf("%s", s);
  int ans = 0;
  for (int i = 0; i < k; ++i)
    (ans += ((s[i] == '+') ? 1ll : -1ll) * fp(a, n - i) % M * fp(b, i) % M) %=
        M;
  int after = (long long)fp(fp(a, k), M - 2) * fp(b, k) % M;
  if (after > 1)
    after = ((long long)(fp(after, (n + 1) / k) - after)) *
            fp(after - 1, M - 2) % M;
  else
    after = (n + 1 - k) / k;
  printf("%lld", (((long long)ans * (after + 1) % M) + M) % M);
}

### Prompt

Please create a solution in CPP 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 K = 1e5 + 7, M = 1e9 + 9;
int fp(int x, int y) {
  int ret = 1;
  for (; y; y >>= 1, x = (long long)x * x % M)
    if (y & 1) ret = (long long)ret * x % M;
  return ret;
}
int n, a, b, k;
char s[K];
int main() {
  scanf("%d%d%d%d", &n, &a, &b, &k);
  scanf("%s", s);
  int ans = 0;
  for (int i = 0; i < k; ++i)
    (ans += ((s[i] == '+') ? 1ll : -1ll) * fp(a, n - i) % M * fp(b, i) % M) %=
        M;
  int after = (long long)fp(fp(a, k), M - 2) * fp(b, k) % M;
  if (after > 1)
    after = ((long long)(fp(after, (n + 1) / k) - after)) *
            fp(after - 1, M - 2) % M;
  else
    after = (n + 1 - k) / k;
  printf("%lld", (((long long)ans * (after + 1) % M) + M) % M);
}

```