Camels
Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps,representing them as polylines in the plane. Each polyline consists of n vertices withcoordinates (x1, y1), (x2, y2), ..., (xn, yn). The first vertex has a coordinate x1 = 1, the second— x2 = 2, etc. Coordinates yi might be any, but should satisfy the following conditions:
- there should be t humps precisely, i.e. such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 < yj > yj + 1,
- there should be precisely t - 1 such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 > yj < yj + 1,
- no segment of a polyline should be parallel to the Ox-axis,
- all yi are integers between 1 and 4.
For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn'tknow how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.
Input
The first line of input contains the number of testcases , Ntest.
Each testcase contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).
Output
For each testcase ,output the required amount of camels with t humps.
Example
Input:
1
6 1
Output:
6
NoteIn the first sample test sequences of y-coordinates for six camels are: 123421, 123431,
123432, 124321, 134321 и 234321 (each digit corresponds to one value of yi).