#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 9;
void add(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  if (a < 0) a += MOD;
}
int mul(int a, int b) { return (long long)a * b % MOD; }
int power(int a, int b) {
  if (b < 0) return 0;
  int ans = 1;
  while (b > 0) {
    if (b & 1) ans = mul(ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return ans;
}
int main() {
  int n, a, b, k;
  cin >> n >> a >> b >> k;
  string s;
  cin >> s;
  int cc = 0;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '+') {
      add(cc, mul(power(a, n - i), power(b, i)));
    } else {
      add(cc, -mul(power(a, n - i), power(b, i)));
    }
  }
  int p = (n + 1) / k;
  int x = mul(power(b, k), power(power(a, k), MOD - 2));
  if (x == 1) {
    cout << mul(cc, p) << endl;
    return 0;
  }
  int dd = 1;
  add(dd, -x);
  int nn = 1;
  add(nn, -power(x, p));
  int ans = mul(cc, mul(nn, power(dd, MOD - 2)));
  cout << ans << endl;
}

### Prompt

In cpp, your task is to solve 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;
void add(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  if (a < 0) a += MOD;
}
int mul(int a, int b) { return (long long)a * b % MOD; }
int power(int a, int b) {
  if (b < 0) return 0;
  int ans = 1;
  while (b > 0) {
    if (b & 1) ans = mul(ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return ans;
}
int main() {
  int n, a, b, k;
  cin >> n >> a >> b >> k;
  string s;
  cin >> s;
  int cc = 0;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '+') {
      add(cc, mul(power(a, n - i), power(b, i)));
    } else {
      add(cc, -mul(power(a, n - i), power(b, i)));
    }
  }
  int p = (n + 1) / k;
  int x = mul(power(b, k), power(power(a, k), MOD - 2));
  if (x == 1) {
    cout << mul(cc, p) << endl;
    return 0;
  }
  int dd = 1;
  add(dd, -x);
  int nn = 1;
  add(nn, -power(x, p));
  int ans = mul(cc, mul(nn, power(dd, MOD - 2)));
  cout << ans << endl;
}

```