You are given a permutation aaa of size nnn and you should perform nnn operations on i

An inversion in an array aaa is a pair of indices (i,j)(i,j)(i, j) such that i>ji>ji > j and ai<ajai<aja_{i} < a_{j}.

The i-th element of p will be denoted as p

For all pairs of distinct integers i, j between 1 and n

he wrote the number ai, j = min(pi, pj)

Petya's got n non-transparent glasses

standing in a row

First Petya puts a marble under the glass in position s

and you want to find out the first bad one,

you are fighting against nnn monsters

Monster number iii has aiaia_i health points

monster is alive while it has at least 111 health point.

The string www and the integer p

the price of the string abca is 1+2+3+1=71+2+3+1=71+2+3+1=7

Remove the minimal number of letters from www so that its price becomes less than or equal to ppp and print the resulting string