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
import java.util.Scanner;


public class CFPROBA {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input = new Scanner(System.in);
		int length = input.nextInt();
		int n = input.nextInt();
		int m = input.nextInt();
		input.nextLine();
		String inputString = input.nextLine();
		for(int a = 0; a <=100; a++){
			for(int b = 0; b<= 100; b++){
				if(a * n + b * m == inputString.length()){
					System.out.println(a+b);
					for(int c = 0; c < a; c++){
						System.out.println(inputString.substring(c*n, (c+1) * n));
					}
					for(int c = 0; c < b; c++){

						System.out.println(inputString.substring(a*n+c*m, a*n+(c+1) * m));
					}
					System.exit(0);
				}
			}
		}
		System.out.println(-1);
	}

}
