Conveyor Batch Prefix Flip

An automated sorting line carries crates, each stamped with a single lowercase letter, past a re-orientation station in a fixed left-to-right order. The station processes the belt in consecutive batches of 2k crates: for each batch, a robotic arm grips the first k crates and flips their order end-to-end, then lets the remaining crates in that batch roll through untouched. Given the full sequence of letters on the belt and the batch size parameter k, determine the final left-to-right order of letters after every batch has been processed. A trailing batch with fewer than k crates has all of its crates flipped; a trailing batch with between k and 2k crates has exactly its first k crates flipped and the rest left as-is.

Input format

• Line 1: a string s of lowercase English letters — the crate sequence (1 ≤ |s| ≤ 10000).
• Line 2: an integer k (1 ≤ k ≤ 10000).

Output format

The resulting string after processing every batch, on one line.

Constraints

• 1 ≤ |s| ≤ 10000, lowercase English letters only.
• 1 ≤ k ≤ 10000; k may exceed |s|, in which case the whole string is treated as one (possibly partial) trailing batch.

abcdefg
2

bacdfeg

abcd
2

bacd