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B - Broken Rounding

Score : $200$ points

Problem Statement

Given a non-negative integer $X$, perform the following operation for $i=1,2,\dots,K$ in this order and find the resulting $X$.

• Round $X$ off to the nearest $10^i$.
  • Formally, replace $X$ with $Y$ that is "the largest multiple of $10^i$ that minimizes $|Y-X|$."
  • Here are some examples:
    • Rounding $273$ off to the nearest $10^2$ yields $300$.
    • Rounding $999$ off to the nearest $10^3$ yields $1000$.
    • Rounding $100$ off to the nearest $10^{10}$ yields $0$.
    • Rounding $1015$ off to the nearest $10^1$ yields $1020$.

Constraints

• $X$ and $K$ are integers.
• $0 \le X < 10^{15}$
• $1 \le K \le 15$

Input

The input is given from Standard Input in the following format:

$X$ $K$

Output

Print the answer as an integer.

2048 2

2100

$X$ changes as $2048 \rightarrow 2050 \rightarrow 2100$ by the operations.

1 15

0

999 3

1000

314159265358979 12

314000000000000

$X$ may not fit into a $32$-bit integer type.