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:
AdjBC(011101101) = 3
AdjBC(111101101) = 4
AdjBC(010101010) = 0

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:
10
1 5 2
2 20 8
3 30 17
4 40 24
5 50 37
6 60 52
7 70 59
8 80 73
9 90 84
10 100 90
Output:
1 6
2 63426
3 1861225
4 168212501
5 44874764
6 160916
7 22937308
8 99167
9 15476
10 23076518

hide comments
codehead1997: 2018-04-20 11:40:02

my 49th
AC in go !!!!
took me 3 hrs..

shivr1: 2018-03-15 04:43:47

dp

Last edit: 2018-03-22 12:07:45
pallindromeguy: 2018-03-03 13:30:08

nice problem.. took 3 hrs but AC in one go ;)

mohit_aggarwal: 2018-02-19 07:01:48

My 50th ;-p
AC in one Go !!

Last edit: 2018-02-19 07:02:15
mrpandey: 2018-01-21 18:34:10

I did it in O(n-k) time complexity. A 3-line for loop is what it took. For me it was a pure maths question. No need of DP. Try using combinatorics.

javafreak: 2017-12-20 09:06:11

2-d dp, along with bit, time complexity - (n^2)logn per test case.

gaurav_76170: 2017-12-12 13:44:01

3D dp top down approach will work

sharif ullah: 2017-09-30 07:09:01

3D dp. just draw 0/1 knapsack topdown approach of this problem with pen&&paper

resli_basha: 2017-07-31 08:52:09

AC in one go!! in 0.00 time
Nice Dp!!.

rajeev_mnnit: 2017-05-10 16:18:32

Nice one :)


Added by:Tamer
Date:2009-11-14
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC PERL6 SQLITE VB.NET
Resource:ACM Greater New York Regional Contest 2009