#include <bits/stdc++.h>
using namespace std;
long long n, a, b, k, has, x, y, z, e = 1000000009, rep;
string s;
long long bm(long long a, long long b) {
  if (b == 0) return 1;
  long long t = bm(a, b / 2);
  if (b % 2 == 1)
    return a * (t * t % e) % e;
  else
    return t * t % e;
}
long long inv(long long a) { return bm(a, e - 2); }
int main() {
  cin >> n >> a >> b >> k >> s;
  rep = (n + 1) / k;
  for (int i = 0; i < k; i++) {
    long long p;
    if (s[i] == '+')
      p = 1;
    else
      p = -1;
    x = (x % e + p * (bm(a, n - i) % e) * (bm(b, i) % e) + e) % e;
  }
  y = bm(b * inv(a) % e, k);
  long long ats, bwh;
  ats = bm(y, rep) - 1;
  bwh = y - 1;
  if (y == 1)
    has = ((x % e) * (rep % e)) % e;
  else
    has = ((x % e) * (ats * inv(bwh) % e)) % e;
  if (has < 0) has += e;
  cout << has << endl;
}

### 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;
long long n, a, b, k, has, x, y, z, e = 1000000009, rep;
string s;
long long bm(long long a, long long b) {
  if (b == 0) return 1;
  long long t = bm(a, b / 2);
  if (b % 2 == 1)
    return a * (t * t % e) % e;
  else
    return t * t % e;
}
long long inv(long long a) { return bm(a, e - 2); }
int main() {
  cin >> n >> a >> b >> k >> s;
  rep = (n + 1) / k;
  for (int i = 0; i < k; i++) {
    long long p;
    if (s[i] == '+')
      p = 1;
    else
      p = -1;
    x = (x % e + p * (bm(a, n - i) % e) * (bm(b, i) % e) + e) % e;
  }
  y = bm(b * inv(a) % e, k);
  long long ats, bwh;
  ats = bm(y, rep) - 1;
  bwh = y - 1;
  if (y == 1)
    has = ((x % e) * (rep % e)) % e;
  else
    has = ((x % e) * (ats * inv(bwh) % e)) % e;
  if (has < 0) has += e;
  cout << has << endl;
}

```