CT14E - Camels

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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 with coordinates (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 ≤ jn - 1), so that yj - 1 < yj > yj + 1,
• there should be precisely t - 1 such indexes j (2 ≤ jn - 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't know 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 test cases, N.

Each test case contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).

Output

For each testcase, output the required number of camels with t humps.

Example

```Input:
1
6 1

Output:
6```

Note In the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 and 234321 (each digit corresponds to one value of yi).