## GNYR09F - Adjacent Bit Counts

For a string of n bits x1,x2,x3,...,Xn the adjacent bit count of the string (AdjBC(x)) is given by

X1*X2 + X2*X3 + X3*X4 + ... + Xn-1 * Xn

which counts the number of times a 1 bit is adjacent to another 1 bit. For example:

Write a program which takes as input integers n and k and returns the number of bit strings x of n bits (out of 2ⁿ) that satisfy AdjBC(x) = k. For example, for 5 bit strings, there are 6 ways of getting AdjBC(x) = 2:
11100, 01110, 00111, 10111, 11101, 11011

### Input

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (k) giving the desired adjacent bit count. The number of bits (n) will not be greater than 100 and the parameters n and k will be chosen so that the result will fit in a signed 32-bit integer.

### Output

For each data set there is one line of output. It contains the data set number followed by a single space, followed by the number of n-bit strings with adjacent bit count equal to k.

### Example

```Input:
101 5 22 20 83 30 174 40 245 50 376 60 527 70 598 80 739 90 8410 100 90
```
```Output:
1 62 634263 18612254 1682125015 448747646 1609167 229373088 991679 1547610 23076518
``` karthik1997: 2016-06-18 19:59:47 For Beginners striving for the subcase : Solve @www.spoj.com/problems/PERMUT1 First. and You can easily figure out the sub cases ... SImple 3D Dp with O(N*N*2) complexity . PS My complexity itself suggests the required space complexity tooo :D .... Ravi: 2016-03-24 21:51:24 precompute + dp O(n^2) Fantastic Dp :) lakshay_v06: 2016-03-24 13:12:22 AC in one go! O(n^2) : 0.00 <- :D anshal dwivedi: 2016-01-05 17:24:46 yo!AC in one go...! Nice One ..:) Aswin Siva: 2015-12-30 06:48:00 Any other (trivial) approach other than 3D DP ? Any Hints... Sarthak Munshi: 2015-10-09 17:17:52 First time AC . Generate pattern for n=1..10 and k=1..10 using brute force . Observe pattern . Then easy DP . sneh shikhar: 2015-08-25 18:35:53 3D DP :* BOTTOM UP!! arun: 2015-08-02 07:53:31 @sanchit 10111 & 11101 :.Mohib.:: 2015-06-25 01:57:48 Great que for beginners in dp like me...!! TgTtv: 2015-02-19 01:50:19 Recursion fits in the constrains. I wonder, if there is formula based solution.