B'Let f(x,y) be the number of carries of x+y in binary (i. e. f(x,y)=g(x)+g(y)-g(x+y) , where g(x) is the number of ones in the binary representation of x ). Given two integers n and k , find the number of ordered pairs (a,b) such that 0 <= q a,b < 2^n , and f(a,b) equals k . Note that for a ne b , (a,b) and (b,a) are considered as two different pairs. As this number may be large, output it modulo 10^9+7 . The only line of each test contains two integers n and k ( 0 <= q k<n <= q 10^6 ). Output a single integer -- the answer modulo 10^9+7 . Here are some examples for understanding carries: begin{aligned} & begin{array}{r} 1_{ }1_{ }1 + _{1}1_{ }0_{ }0 hline 1_{ }0_{ }1_{ }1 end{array} & begin{array}{r} 1_{ }0_{ }1 + _{ }0_{ }0_{1}1 hline 0_{ }1_{ }1_{ }0 end{array} & & begin{array}{r} 1_{ }0_{ }1 + _{1}0_{1}1_{1}1 hline 1_{ }0_{ }0_{ }0 end{array} end{aligned} So f(7,4)=1 , f(5,1)=1 and f(5,3)=3 . In the first test case, all the pairs meeting the constraints are (1,1),(1,5),(2,2),(2,3),(3,2),(4,4),(4,5),(4,6),(4,7),(5,1),(5,4),(5,6),(6,4),(6,5),(7,4) . '...