Joisino has a lot of red and blue bricks and a large box. She will build a tower of these bricks in the following manner.

First, she will pick a total of N bricks and put them into the box. Here, there may be any number of bricks of each color in the box, as long as there are N bricks in total. Particularly, there may be zero red bricks or zero blue bricks. Then, she will repeat an operation M times, which consists of the following three steps:

* Take out an arbitrary brick from the box.
* Put one red brick and one blue brick into the box.
* Take out another arbitrary brick from the box.



After the M operations, Joisino will build a tower by stacking the 2 \times M bricks removed from the box, in the order they are taken out. She is interested in the following question: how many different sequences of colors of these 2 \times M bricks are possible? Write a program to find the answer. Since it can be extremely large, print the count modulo 10^9+7.

Constraints

* 1 \leq N \leq 3000
* 1 \leq M \leq 3000

Input

Input is given from Standard Input in the following format:


N M


Output

Print the count of the different possible sequences of colors of 2 \times M bricks that will be stacked, modulo 10^9+7.

Examples

Input

2 3


Output

56


Input

1000 10


Output

1048576


Input

1000 3000


Output

693347555
#include <bits/stdc++.h>
using namespace std;
const int N = 3005, MOD = 1e9 + 7;
int f[N][N][2];
void upd(int &x, int y) { (x += y) %= MOD; }
int main() {
	int n, m;
	scanf("%d%d", &n, &m);
	for (int i = 0; i <= n; ++ i) f[0][i][i == 0] = 1;
	for (int i = 1; i <= m; ++ i) {
		for (int j = 0; j <= n; ++ j) {
			for (int k = 0; k <= 1; ++ k) {
				int g = f[i - 1][j][k];
				if (j > 0) upd(f[i][j - 1][k | (j == 1)], g);
				if (j > 0) upd(f[i][j][k | (j == 1)], g);
				if (j < n) upd(f[i][j][k], g);
				if (j < n) upd(f[i][j + 1][k], g);
			}
		}
	}
	int ans = 0;
	for (int i = 0; i <= n; ++ i) upd(ans, f[m][i][1]);
	printf("%d\n", ans);
}
