Harmony

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

inputFormat

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

outputFormat

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

样例

998244353 99824435

549034394