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>
int main() {
  int n, p, q;
  std::cin >> n >> p >> q;
  std::string s;
  std::cin >> s;
  bool ok = false;
  for (int k1 = 0; k1 * p <= n; ++k1) {
    for (int k2 = 0; k2 * q + k1 * p <= n; ++k2) {
      if (k1 * p + k2 * q == n) {
        ok = true;
        std::cout << (k1 + k2) << '\n';
        for (int i = 0; i < k1; ++i)
          std::cout << std::string(s.begin() + i * p, s.begin() + i * p + p)
                    << '\n';
        for (int i = 0; i < k2; ++i)
          std::cout << std::string(s.begin() + k1 * p + i * q,
                                   s.begin() + k1 * p + i * q + q)
                    << '\n';
        break;
      }
    }
    if (ok) break;
  }
  if (!ok) std::cout << (-1) << '\n';
  return 0;
}
