#include <bits/stdc++.h>
using namespace std;
const int64_t M = 1e9 + 9;
int64_t n, a, b, k;
string s;
int64_t power(int64_t x, int64_t y) {
  int64_t ret = 1;
  while (y) {
    if (y & 1) ret = ret * x % M;
    x = x * x % M;
    y >>= 1;
  }
  return ret;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> b >> a >> k;
  cin >> s;
  int64_t ans = 0;
  for (int64_t i = 0; i < k; i++)
    (ans += (s[i] == '-' ? -1 : +1) * power(a, i) % M * power(b, n - i) % M) %=
        M;
  int64_t z = power(a, k) * power(power(b, M - 2), k) % M;
  z = (z + M) % M;
  if (z == 1)
    ans = ans * ((n + 1) / k) % M;
  else
    ans = ans * ((power(z, (n + 1) / k) - 1) * power(z - 1, M - 2) % M) % M;
  ans = (ans + M) % M;
  cout << ans << endl;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 int64_t M = 1e9 + 9;
int64_t n, a, b, k;
string s;
int64_t power(int64_t x, int64_t y) {
  int64_t ret = 1;
  while (y) {
    if (y & 1) ret = ret * x % M;
    x = x * x % M;
    y >>= 1;
  }
  return ret;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> b >> a >> k;
  cin >> s;
  int64_t ans = 0;
  for (int64_t i = 0; i < k; i++)
    (ans += (s[i] == '-' ? -1 : +1) * power(a, i) % M * power(b, n - i) % M) %=
        M;
  int64_t z = power(a, k) * power(power(b, M - 2), k) % M;
  z = (z + M) % M;
  if (z == 1)
    ans = ans * ((n + 1) / k) % M;
  else
    ans = ans * ((power(z, (n + 1) / k) - 1) * power(z - 1, M - 2) % M) % M;
  ans = (ans + M) % M;
  cout << ans << endl;
  return 0;
}

```