#include <bits/stdc++.h>
using namespace std;
const int p = 1000000009;
int n, a, b, k;
char s[100005];
int ksm(int x, int t, int y = 1) {
  while (t) {
    if (t & 1) y = 1ll * y * x % p;
    x = 1ll * x * x % p;
    t >>= 1;
  }
  return y;
}
signed main() {
  cin >> n >> a >> b >> k >> s + 1;
  int x = ksm(a, n), y = 1, a1 = 0;
  for (int i = 1; i <= k; i++) {
    if (s[i] == '-')
      a1 = (a1 + p - 1ll * x * y % p) % p;
    else
      a1 = (a1 + 1ll * x * y % p) % p;
    x = 1ll * x * ksm(a, p - 2) % p;
    y = 1ll * y * b % p;
  }
  int q = 1ll * ksm(b, k) * ksm(ksm(a, k), p - 2) % p;
  if (q == 1)
    cout << 1ll * a1 * ((n + 1) / k) % p << '\n';
  else
    cout << 1ll * a1 * ((ksm(q, (n + 1) / k) % p + p - 1) % p) % p *
                ksm((q + p - 1) % p, p - 2) % p
         << '\n';
}

### 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 p = 1000000009;
int n, a, b, k;
char s[100005];
int ksm(int x, int t, int y = 1) {
  while (t) {
    if (t & 1) y = 1ll * y * x % p;
    x = 1ll * x * x % p;
    t >>= 1;
  }
  return y;
}
signed main() {
  cin >> n >> a >> b >> k >> s + 1;
  int x = ksm(a, n), y = 1, a1 = 0;
  for (int i = 1; i <= k; i++) {
    if (s[i] == '-')
      a1 = (a1 + p - 1ll * x * y % p) % p;
    else
      a1 = (a1 + 1ll * x * y % p) % p;
    x = 1ll * x * ksm(a, p - 2) % p;
    y = 1ll * y * b % p;
  }
  int q = 1ll * ksm(b, k) * ksm(ksm(a, k), p - 2) % p;
  if (q == 1)
    cout << 1ll * a1 * ((n + 1) / k) % p << '\n';
  else
    cout << 1ll * a1 * ((ksm(q, (n + 1) / k) % p + p - 1) % p) % p *
                ksm((q + p - 1) % p, p - 2) % p
         << '\n';
}

```