Counting Faces in a Hypercube

In an $a$-dimensional hypercube, the number of $b$-dimensional faces is given by the formula [ F(a, b) = \binom{a}{b} \cdot 2^{a-b}, ] where (\binom{a}{b}) is the binomial coefficient. For example, a square (2-dimensional hypercube) has 4 vertices (0-dimensional faces), 4 edges (1-dimensional faces), and 1 square (2-dimensional face); a cube (3-dimensional hypercube) has 8 vertices, 12 edges, 6 faces, and 1 cube.

Given two integers $a$ and $b$ (with $0 \le b \le a$), compute the number of $b$-dimensional faces contained in an $a$-dimensional hypercube, modulo $10^9+7$.

inputFormat

The input consists of a single line containing two space-separated integers $a$ and $b$.

outputFormat

Output a single integer representing the number of $b$-dimensional faces in an $a$-dimensional hypercube modulo $10^9+7$.

sample

3 1

12