#include <bits/stdc++.h>
using namespace std;
const long long mod = (1e9) + 9;
long long n, a, b, k, ans, t;
char s[100010];
long long ksm(long long x, long long y) {
  if (y == 0) return 1;
  if (y == 1) return x % mod;
  long long res = ksm(x, y / 2);
  res = res * res % mod;
  if (y % 2 == 1) res = res * x % mod;
  return res;
}
int main() {
  scanf("%lld %lld %lld %lld %s", &n, &a, &b, &k, s + 1);
  n++;
  for (int i = 1; i <= k; i++) {
    long long tmp = ksm(a, n - i) * ksm(b, i - 1) % mod;
    if (s[i] == '+')
      ans += tmp;
    else if (s[i] == '-')
      ans -= tmp;
    while (ans < 0) ans += mod;
    ans %= mod;
  }
  long long x = ksm(b, k) * ksm(ksm(a, k), mod - 2) % mod;
  if (x == 1)
    t = n / k;
  else
    t = (ksm(x, n / k) - 1) * ksm(x - 1, mod - 2) % mod;
  ans = ans * t % mod;
  printf("%I64d\n", ans);
  return 0;
}

### 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 long long mod = (1e9) + 9;
long long n, a, b, k, ans, t;
char s[100010];
long long ksm(long long x, long long y) {
  if (y == 0) return 1;
  if (y == 1) return x % mod;
  long long res = ksm(x, y / 2);
  res = res * res % mod;
  if (y % 2 == 1) res = res * x % mod;
  return res;
}
int main() {
  scanf("%lld %lld %lld %lld %s", &n, &a, &b, &k, s + 1);
  n++;
  for (int i = 1; i <= k; i++) {
    long long tmp = ksm(a, n - i) * ksm(b, i - 1) % mod;
    if (s[i] == '+')
      ans += tmp;
    else if (s[i] == '-')
      ans -= tmp;
    while (ans < 0) ans += mod;
    ans %= mod;
  }
  long long x = ksm(b, k) * ksm(ksm(a, k), mod - 2) % mod;
  if (x == 1)
    t = n / k;
  else
    t = (ksm(x, n / k) - 1) * ksm(x - 1, mod - 2) % mod;
  ans = ans * t % mod;
  printf("%I64d\n", ans);
  return 0;
}

```