#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 9;
const int N = 1e5 + 7;
int qp(int a, int b = MOD - 2) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = 1LL * ans * a % MOD;
    a = 1LL * a * a % MOD;
    b >>= 1;
  }
  return ans;
}
int M(int a) {
  if (a < 0) a += MOD;
  if (a >= MOD) a -= MOD;
  return a;
}
char s[N];
int main() {
  int n, a, b, k;
  scanf("%d%d%d%d", &n, &a, &b, &k);
  int q = 1LL * qp(qp(a, k)) * qp(b, k) % MOD;
  scanf("%s", s);
  int a1 = 0;
  for (int i = 0; i < k; i++) {
    int x = ((s[i] == '+') ? 1 : -1);
    a1 = M(a1 + 1LL * x * qp(a, n - i) % MOD * qp(b, i) % MOD);
  }
  if (q == 1) {
    int ans = 1LL * a1 * (n + 1) / k % MOD;
    printf("%d\n", ans);
    return 0;
  }
  int inv = qp(q - 1);
  int ans = 1LL * a1 * (qp(q, (n + 1) / k) - 1) % MOD * inv % MOD;
  printf("%d\n", ans);
  return 0;
}

### Prompt

Please formulate 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 = 1e9 + 9;
const int N = 1e5 + 7;
int qp(int a, int b = MOD - 2) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = 1LL * ans * a % MOD;
    a = 1LL * a * a % MOD;
    b >>= 1;
  }
  return ans;
}
int M(int a) {
  if (a < 0) a += MOD;
  if (a >= MOD) a -= MOD;
  return a;
}
char s[N];
int main() {
  int n, a, b, k;
  scanf("%d%d%d%d", &n, &a, &b, &k);
  int q = 1LL * qp(qp(a, k)) * qp(b, k) % MOD;
  scanf("%s", s);
  int a1 = 0;
  for (int i = 0; i < k; i++) {
    int x = ((s[i] == '+') ? 1 : -1);
    a1 = M(a1 + 1LL * x * qp(a, n - i) % MOD * qp(b, i) % MOD);
  }
  if (q == 1) {
    int ans = 1LL * a1 * (n + 1) / k % MOD;
    printf("%d\n", ans);
    return 0;
  }
  int inv = qp(q - 1);
  int ans = 1LL * a1 * (qp(q, (n + 1) / k) - 1) % MOD * inv % MOD;
  printf("%d\n", ans);
  return 0;
}

```