Check if the bit is set

Given an integer n and a number p which is a power of 2, you are asked to find out if the bit corresponding to p is set to 1 in n.

Input

The input contains two integers n (1 ≤ n ≤ ) and p (1 ≤ p ≤ ).

Output

The program should print Yes if the corresponding bit is set and No otherwise.

Examples

Input

Output

9 8

Yes

9 4

No

9 1

Yes

311 4

Yes

311 8

No

Explanation

  1. 9 → 1001, 8 → 1000 ⇒ the most significant bit is set which corresponds to 8

  2. 9 → 1001, 4 → 100 ⇒ the 3rd (from the right) bit is not set

  3. 9 → 1001, 1 → 1 ⇒ the least significant bit is set which corresponds to 1

  4. 311 → 100110111, 4 → 100 ⇒ the 3rd (from the right) bit is set

  5. 311 → 100110111, 8 → 1000 ⇒ the 4th (from the right) bit is not set

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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