A teacher of mathematics asks schoolboys to make up an arithmetic expression with value
equal to N. It is possible to use natural numbers <= K, operations '+' and '*',
and brackets. Petya want to make up an expression with minimal number of characters.
Write program to help Petya.
Input:
First line contains two natural numbers N (1<=N<=10000) - expression's value,
and K (1<=K<=10000) - maximal number for using in expression.
Output:
Expression with minimal number of characters, written on a single line.
If there are several solutions, write any of them.
Examples:
-------------------------------------------------------------------------
|STDIN | STDOUT |explanation: |
| | |length of expression|
-------------------------------------------------------------------------
|7 3 |3+1+3 |5 |
-------------------------------------------------------------------------
|15 20 |15 |2 |
-------------------------------------------------------------------------
|176 1 |(1+1+1+1)*(1+1+1+1)*(1+1+(1+1+1)*(1+1+1)) |41 |
-------------------------------------------------------------------------
|
