Description

Elements in $0$-dimensional space are points, which is beyond doubt.

• $2$ elements of $0$-dimensional space can form a $1$-dimensional element, a line segment.
• $4$ elements of $1$-dimensional space can form a $2$-dimensional element, a square.
• $6$ elements of $2$-dimensional space can form a $3$-dimensional element, a cube.
• $8$ elements of $3$-dimensional space can form a $4$-dimensional element, a hypercube.

…

• In a square, there are $4$ points (vertices), $4$ line segments (edges), and $1$ square.
• In a cube, there are $8$ points (vertices), $12$ line segments (edges), $6$ squares (faces), and $1$ cube.

…

Our problem is: given $a$ and $b$, find how many $b$-dimensional elements are contained in an $a$-dimensional element. The answer may be large; output it modulo $10^9+7$.

Input Format

Two integers $a,b$, separated by a space.

Output Format

One integer, the answer.

3 1

12

Hint

Sample Explanation

The $3$-dimensional element is a cube, and the $1$-dimensional element is a line segment. What is required is the number of edges in a cube, which is $12$.

Constraints

• For $5\%$ of the data, $a,b \le 1$.
• For $10\%$ of the data, $a,b \le 2$.
• For $20\%$ of the data, $a,b \le 3$.
• For $35\%$ of the data, $a,b \le 4$.
• For $70\%$ of the data, $a,b \le 1000$.
• For $100\%$ of the data, $0 \le a,b \le 100000$.

In addition, for $15\%$ of the testdata, $b=0$; for $10\%$ each, $b=1$ or $b=2$.

Tip

It is not guaranteed that $a \ge b$.

Translated by ChatGPT 5