13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T7be,

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 $$$0 \leq a,b \lt 2^n$$$, 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 $$$10^9+7$$$.

Input

The only line of each test contains two integers $$$n$$$ and $$$k$$$ ($$$0\leq k \lt n\leq 10^6$$$).

Output

Output a single integer — the answer modulo $$$10^9+7$$$.

Note

Here are some examples for understanding carries:

$$$$$$ \begin{aligned} &\begin{arra

Carry Bit

Examples