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>
void STRIKE(char chuoi[], int solan1, int dodaidoan1, int solan2,
            int dodaidoan2) {
  printf("%d\n", solan1 + solan2);
  char temp[101];
  strcpy(temp, chuoi);
  char d[101];
  int dem = 0;
  for (int i = 1; i <= solan1; i++) {
    for (int j = 1; j <= dodaidoan1; j++) {
      printf("%c", temp[dem]);
      dem++;
    }
    printf("\n");
  }
  for (int i = 1; i <= solan2; i++) {
    for (int j = 1; j <= dodaidoan2; j++) {
      printf("%c", temp[dem]);
      dem++;
    }
    printf("\n");
  }
}
bool Kiemtra(char s[], int x, int y, int n) {
  int dem = 0;
  while (n > 0) {
    n -= x;
    dem++;
    if (n % y == 0 && n >= 0) {
      STRIKE(s, dem, x, n / y, y);
      return true;
    }
  }
  return false;
}
int main() {
  int n, q, k;
  char s[101], temp;
  scanf("%d%d%d", &n, &q, &k);
  scanf("%c", &temp);
  gets(s);
  bool c;
  c = Kiemtra(s, q, k, n);
  if (c == false) c = Kiemtra(s, k, q, n);
  if (c == false) printf("-1");
}
