Alice in linear land

Alice lives on a line. Today, she will travel to some place in a mysterious vehicle. Initially, the distance between Alice and her destination is D. When she input a number x to the vehicle, it will travel in the direction of the destination by a distance of x if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than x.

Alice made a list of N numbers. The i-th number in this list is d_i. She will insert these numbers to the vehicle one by one.

However, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after N moves.

She has Q plans to do this, as follows:

• Rewrite only the q_i-th number in the list with some integer so that Alice will not reach the destination.

Write a program to determine whether each plan is feasible.

Constraints

• 1≤ N ≤ 5*10^5
• 1≤ Q ≤ 5*10^5
• 1≤ D ≤ 10^9
• 1≤ d_i ≤ 10^9(1≤i≤N)
• 1≤ q_i ≤ N(1≤i≤Q)
• D and each d_i are integers.

Input

Input is given from Standard Input in the following format:

N D d_1 d_2 ... d_N Q q_1 q_2 ... q_Q

Output

Print Q lines. The i-th line should contain YES if the i-th plan is feasible, and NO otherwise.

Examples

Input

4 10 3 4 3 3 2 4 3

Output

NO YES

Input

5 9 4 4 2 3 2 5 1 4 2 3 5

Output

YES YES YES YES YES

Input

6 15 4 3 5 4 2 1 6 1 2 3 4 5 6

Output

NO NO YES NO NO YES

inputFormat

input a number x to the vehicle, it will travel in the direction of the destination by a distance of x if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than x.

Alice made a list of N numbers. The i-th number in this list is d_i. She will insert these numbers to the vehicle one by one.

However, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after N moves.

She has Q plans to do this, as follows:

• Rewrite only the q_i-th number in the list with some integer so that Alice will not reach the destination.

Write a program to determine whether each plan is feasible.

Constraints

• 1≤ N ≤ 5*10^5
• 1≤ Q ≤ 5*10^5
• 1≤ D ≤ 10^9
• 1≤ d_i ≤ 10^9(1≤i≤N)
• 1≤ q_i ≤ N(1≤i≤Q)
• D and each d_i are integers.

Input

Input is given from Standard Input in the following format:

N D d_1 d_2 ... d_N Q q_1 q_2 ... q_Q

outputFormat

Output

Print Q lines. The i-th line should contain YES if the i-th plan is feasible, and NO otherwise.

Examples

Input

4 10 3 4 3 3 2 4 3

Output

NO YES

Input

5 9 4 4 2 3 2 5 1 4 2 3 5

Output

YES YES YES YES YES

Input

6 15 4 3 5 4 2 1 6 1 2 3 4 5 6

Output

NO NO YES NO NO YES

样例

5 9
4 4 2 3 2
5
1 4 2 3 5

YES
YES
YES
YES
YES

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