The Ninja Girl Never Stops

The Princess Waraku show Izuna is helping with today is an interactive event! Izuna, an audience member, becomes the hero, overcomes obstacles in the film village, and rescues the kidnapped princess!

It is supposed to be a participatory performance where we save the princess... But instead of Princess Waraku, Ibuki, who has nothing to do with the show, has been kidnapped?!

Izuna followed the kidnappers' escape route with the Ninjutsu Research Club, and we arrived at the Trick House!

The president went in ahead of us just like that, and Izuna ended up wandering around the Trick House for quite a while... But now, at last, we are all together again!

Tsukuyo-dono's solution was simple! If we think of movement inside the Trick House mansion as movement on a grid, we can make a plan without getting lost...! So Izuna decided to model it as follows!

We can think of the Trick House mansion as an isosceles right triangle whose equal sides have length $\frac{N}{2}$! Mathematically... speaking, its two equal sides lie along the positive $x$-axis and the positive $y$-axis of the coordinate plane. Its vertices are therefore $(0, 0)$, , and !

Izuna moves from the starting point at the upper-left vertex $(0, \frac{N}{2})$ to the finish at the lower-right vertex $(\frac{N}{2}, 0)$. On each move, Izuna does one of the following!

The first line contains $N$ and $M$, separated by a space. $(1 \le N \le 200\,000$; $N\text{ is even}$;

Print the number of paths satisfying all the conditions on the first line. Since this number may be very large, output it modulo $1\,000\,000\,007$.