7258: ABC273 —— B - Broken Rounding
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Description
Given a non-negative integer $X$, perform the following operation for $i=1,2,…,K$ 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.
Input
The input is given from Standard Input in the following format:
X K
X K
Output
Print the answer as an integer.
Constraints
X and K are integers.
$0≤X<10^{15}$
$1≤K≤15$
$0≤X<10^{15}$
$1≤K≤15$
Sample 1 Input
2048 2
Sample 1 Output
2100
X changes as 2048→2050→2100 by the operations.
Sample 2 Input
1 15
Sample 2 Output
0
Sample 3 Input
999 3
Sample 3 Output
1000
314159265358979 12
314000000000000
X may not fit into a32-bit integer type.