Bessie has been given n segments on a 1D number line. The i-th segment contains all reals x such that li ≤ x ≤ ri.

Define the union of a set of segments to be the set of all x that are contained within at least one segment. Define the complexity of a set of segments to be the number of connected regions represented in its union, raised to the power of k.

Bessie wants to compute the sum of the complexities over all 2n subsets of the given set of n segments, modulo 109 + 7.

Normally, your job is to help Bessie. But this time, you are Bessie, and there is no one to help you. Help yourself!

Input

The first line contains n (1 ≤ n ≤ 105) and k (2 ≤ k ≤ 10). Each of the next n lines contains two integers li and ri. It is guaranteed that li < ri and all li, ri are distinct integers in the range 1..2n.

Output

Output the answer, modulo 109 + 7.

Example

The complexity of each nonempty subset is written below.

{[1,6]} ⟹ 1, {[2,3]} ⟹ 1, {[4,5]} ⟹ 1

{[1,6],[2,3]} ⟹ 1, {[1,6],[4,5]} ⟹ 1, {[2,3],[4,5]} ⟹ 4

{[1,6],[2,3],[4,5]} ⟹ 1

The answer is 1 + 1 + 1 + 1 + 1 + 4 + 1 = 10.