Problem Statement

There are $N$ non-negative integers written on the blackboard: $A_1, ..., A_N$.

Snuke can perform the following two operations at most $K$ times in total in any order:

• Operation A: Replace each integer $X$ on the blackboard with $X$ divided by $2$, rounded down to the nearest integer.
• Operation B: Replace each integer $X$ on the blackboard with $X$ minus $1$. This operation cannot be performed if one or more $0$s are written on the blackboard.

Find the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo $1,000,000,007$.

Constraints

• $1 \leq N \leq 200$
• $1 \leq A_i \leq 10^{18}$
• $1 \leq K \leq 10^{18}$
• $A_i$ and $K$ are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the number of the different possible combinations of integers written on the blackboard after Snuke performs the operations, modulo $1,000,000,007$.