JOKER1 - Knifes Are Fun

"Do you know, why I use a knife? Guns are too quick. You can't savor all the little emotions. You see, in their last moments, people show you who they really are. So in a way, I know your friends better than you ever did. Would you like to know which of them were cowards?"

Joker has many knifes, and he wants to assign a distinct integer to each knife so he can easily identify them. The i-th knife can have an integer between 1 and maxNumber[i], inclusive.

Return the number of ways he can assign numbers to his knifes, modulo 1,000,000,007. If it's impossible to assign distinct integers to the knifes, print 0.

Input

The first line contains the number of test cases T (1 <= T <= 666)

Each test case has 2 lines - 1st line denotes number of knifes N (1 <= N <= 66) Joker has and the 2nd line denotes the numbers {maxNumber[0]....maxNumber[N-1]} Joker has.

1 <= maxNumber[i] <= 3000

Output

Print the number of ways Joker can assign numbers to his knifes, modulo 1,000,000,007. If it's impossible to assign distinct integers to the knifes, print 0. In last line print the string "KILL BATMAN". Don't print any extra spaces.

Example

Input:
3
1
7
2
5 8
3
2 1 2

Output:
7
35
0
KILL BATMAN

Explanation

  • Test case 1 : Joker can assign any number between 1 and 7, inclusive, to the only knife.
  • Test case 2 : Joker wants you too think !
  • Test case 3 : (1,1,1) (1,1,2) (2,1,1) (2,1,2) are the possible combinations . As the numbering of knifes is not unique so the output is 0.

Added by:Rajarshi Sarkar
Date:2013-02-23
Time limit:0.5s
Source limit:5000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64

hide comments
2013-11-25 13:41:03 abdou_93
Nice problem :D
2013-11-25 13:41:03 Ouditchya Sinha
Nice Question... AC :)
2013-11-25 13:41:03 Kevin Sebastian
@author is it possible for you to give me test cases where my code is failing and can you tell me if my logic is correct

got ac thanx

Last edit: 2013-02-26 04:44:27
2013-11-25 13:41:03 Kevin Sebastian
@author or someone pls pls post tricky test cases..dont knw why im getting wa

EDIT : Problem in code..u are very close to nail down every test case :)

Last edit: 2013-02-26 02:06:56
2013-11-25 13:41:03 Francky
Even in Python I got 0.00s. It would be better with a 2MB input file, (T=1000, N=randint(1,1000), maxLen[i] = randint(1, 1000) ).
Maybe 2s for the slowest language with that constraints.

It's easy, but nice...
2013-11-25 13:41:03 Alex Anderson
I'm guessing maybe the author had an n! solution.

EDIT : NO :)

Last edit: 2013-02-24 03:53:08
2013-11-25 13:41:03 Mitch Schwartz
Why are the constraints so low?
2013-11-25 13:41:03 Alex Anderson
The limits could be larger, but this was alright.
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.