You are given the string s of length n and the numbers p, q. Split the string s to pieces of length p and q.

For example, the string "Hello" for p = 2, q = 3 can be split to the two strings "Hel" and "lo" or to the two strings "He" and "llo".

Note it is allowed to split the string s to the strings only of length p or to the strings only of length q (see the second sample test).

Input

The first line contains three positive integers n, p, q (1 ≤ p, q ≤ n ≤ 100).

The second line contains the string s consists of lowercase and uppercase latin letters and digits.

Output

If it's impossible to split the string s to the strings of length p and q print the only number "-1".

Otherwise in the first line print integer k — the number of strings in partition of s.

Each of the next k lines should contain the strings in partition. Each string should be of the length p or q. The string should be in order of their appearing in string s — from left to right.

If there are several solutions print any of them.

Examples

Input

5 2 3
Hello


Output

2
He
llo


Input

10 9 5
Codeforces


Output

2
Codef
orces


Input

6 4 5
Privet


Output

-1


Input

8 1 1
abacabac


Output

8
a
b
a
c
a
b
a
c
#include <bits/stdc++.h>
using namespace std;
char a[150];
int main() {
  int n, p, q, answer = -1;
  cin >> n >> p >> q;
  cin >> a;
  for (int i = 0; i <= n / p; i++) {
    for (int j = 0; j <= n / q; j++)
      if (i * p + j * q == n) {
        answer = i + j;
        cout << answer << endl;
        for (int x = 0; x < n; x++) {
          cout << a[x];
          if (i && x < i * p && !((x + 1) % p) ||
              j && x >= i * p && !((x - i * p + 1) % q))
            cout << endl;
        }
        break;
      }
    if (answer != -1) break;
  }
  if (answer == -1) cout << -1 << endl;
}
