#include <bits/stdc++.h>
using namespace std;
long long n, a, b, len;
long long aa, ans;
string str;
long long quickpow(long long m, long long n, long long k) {
  m %= k;
  long long b = 1;
  while (n > 0) {
    if (n & 1) b = (b * m) % k;
    n = n >> 1;
    m = (m * m) % k;
  }
  return b;
}
long long f(long long x, long long mod) {
  long long k = mod - 2;
  long long ans = 1;
  while (k) {
    if (k & 1) ans = (ans * x) % mod;
    x = (x * x) % mod;
    k >>= 1;
  }
  return ans;
}
int main() {
  cin >> n >> a >> b >> len;
  cin >> str;
  aa = 0;
  if (n < len) {
    for (int i = 0; i <= n; i++) {
      if (str[i] == '+') {
        ans += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
               1000000009;
        ans %= 1000000009;
      } else {
        ans -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
               1000000009;
        ans = (ans + 1000000009) % 1000000009;
      }
    }
    cout << ans << endl;
    return 0;
  }
  for (int i = 0; i < len; i++) {
    if (str[i] == '+') {
      aa += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
            1000000009;
      aa %= 1000000009;
    } else {
      aa -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
            1000000009;
      aa = (aa + 1000000009) % 1000000009;
    }
  }
  long long turns = (n + 1) / len;
  long long q = quickpow(b * f(a, 1000000009) % 1000000009, len, 1000000009);
  if (q == 1) {
    ans = aa * turns;
    ans %= 1000000009;
  } else {
    ans = aa;
    ans *= (1 - quickpow(q, turns, 1000000009) + 1000000009) % 1000000009;
    ans %= 1000000009;
    ans *= f((1 - q + 1000000009) % 1000000009, 1000000009);
    ans %= 1000000009;
  }
  turns *= len;
  for (int i = turns; i <= n; i++) {
    if (str[i] == '+') {
      ans += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
             1000000009;
      ans %= 1000000009;
    } else {
      ans -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
             1000000009;
      ans = (ans + 1000000009) % 1000000009;
    }
  }
  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;
long long n, a, b, len;
long long aa, ans;
string str;
long long quickpow(long long m, long long n, long long k) {
  m %= k;
  long long b = 1;
  while (n > 0) {
    if (n & 1) b = (b * m) % k;
    n = n >> 1;
    m = (m * m) % k;
  }
  return b;
}
long long f(long long x, long long mod) {
  long long k = mod - 2;
  long long ans = 1;
  while (k) {
    if (k & 1) ans = (ans * x) % mod;
    x = (x * x) % mod;
    k >>= 1;
  }
  return ans;
}
int main() {
  cin >> n >> a >> b >> len;
  cin >> str;
  aa = 0;
  if (n < len) {
    for (int i = 0; i <= n; i++) {
      if (str[i] == '+') {
        ans += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
               1000000009;
        ans %= 1000000009;
      } else {
        ans -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
               1000000009;
        ans = (ans + 1000000009) % 1000000009;
      }
    }
    cout << ans << endl;
    return 0;
  }
  for (int i = 0; i < len; i++) {
    if (str[i] == '+') {
      aa += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
            1000000009;
      aa %= 1000000009;
    } else {
      aa -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
            1000000009;
      aa = (aa + 1000000009) % 1000000009;
    }
  }
  long long turns = (n + 1) / len;
  long long q = quickpow(b * f(a, 1000000009) % 1000000009, len, 1000000009);
  if (q == 1) {
    ans = aa * turns;
    ans %= 1000000009;
  } else {
    ans = aa;
    ans *= (1 - quickpow(q, turns, 1000000009) + 1000000009) % 1000000009;
    ans %= 1000000009;
    ans *= f((1 - q + 1000000009) % 1000000009, 1000000009);
    ans %= 1000000009;
  }
  turns *= len;
  for (int i = turns; i <= n; i++) {
    if (str[i] == '+') {
      ans += (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
             1000000009;
      ans %= 1000000009;
    } else {
      ans -= (quickpow(a, n - i, 1000000009) * quickpow(b, i, 1000000009)) %
             1000000009;
      ans = (ans + 1000000009) % 1000000009;
    }
  }
  cout << ans << endl;
  return 0;
}

```