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;
int a[3], m, n, d[300005], tr[300005];
string s, res[300005];
void setup() {}
void solve() {
  cin >> n >> a[1] >> a[2];
  cin >> s;
  for (int i = 0; i <= n; ++i)
    for (int j = 1; j <= 2; ++j)
      if (d[i] > 0 || i == 0) d[i + a[j]] = d[i] + 1, tr[i + a[j]] = i;
  if (d[n] == 0)
    cout << -1;
  else {
    cout << d[n] << endl;
    while (tr[n] != 0) {
      res[++m] = string(s, tr[n], n - tr[n]);
      n = tr[n];
    }
    res[++m] = string(s, tr[n], n - tr[n]);
    for (int i = m; i >= 1; --i) cout << res[i] << endl;
  }
}
int main() {
  setup();
  solve();
  return 0;
}
