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A. The Text Splitting

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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