We have two distinct integers A and B.

Print the integer K such that |A - K| = |B - K|.

If such an integer does not exist, print IMPOSSIBLE instead.

Constraints

• All values in input are integers.
• $0 \leq A$,\ $B \leq 10^9$
• A and B are distinct.

Input

Input is given from Standard Input in the following format:

A B

Output

Print the integer K satisfying the condition.

If such an integer does not exist, print IMPOSSIBLE instead.

Examples

Input

2 16

Output

9

Input

0 3

Output

IMPOSSIBLE

Input

998244353 99824435

Output

549034394

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