Firefly Flash Absorption Sequence

Along a straight hedge, n fireflies are lined up and numbered 1 to n in order. Firefly i emits a single flash of one lowercase-letter color, given by s[i]. Two fireflies emitting the SAME color are said to be within resonance of each other if the number of positions between them (their index gap) is at most k, measured in the CURRENT line-up -- not the original numbering, since the line-up shrinks over time as described below.

Whenever a resonant same-color pair exists anywhere in the current line-up, the later (right-hand) firefly of that pair is absorbed into the earlier (left-hand) one and permanently leaves the line; the remaining fireflies then close the gap and are re-numbered 1 through the new count, in order, exactly as if that firefly's flash were deleted from a string. If several resonant pairs exist at once, the one whose earlier (left-hand) firefly currently sits furthest to the left is absorbed first; if more than one such pair shares that same left-hand firefly, the one with the nearest right-hand partner is absorbed first. This absorption repeats, always re-checking the current (possibly changed) line-up for new resonant pairs after every single absorption, until no resonant same-color pair remains anywhere.

Given the initial flash colors and k, determine the final surviving sequence of flash colors, left to right.

Input format

• Line 1: a string s of lowercase English letters -- the initial flash colors, left to right.
• Line 2: a single integer k -- the resonance distance threshold.

Output format

A single line: the string of surviving flash colors, left to right, after no resonant pair remains.

Constraints

• 1 <= |s| <= 100
• 1 <= k <= |s|
• s consists only of lowercase English letters.

aabca
2

abca

yybyzybz
2

ybzybz