Dinner Party Socializing

Problem code: SOCIAL

All submissions for this problem are available.

The chef is having a dinner party. He has N chairs and has invited N guests. The chef knows that if the guests are left to their own devices, they tend to sit in the same chairs and socialize with the same people all night. To prevent this, the chef has developed a plan to help people socialize. He will assign each chair a follow-up chair. At predetermined intervals during the party, the chef will ring a bell, instructing all guests to move from their current chair to its follow-up chair.

The chef will assign follow-up chairs randomly, with the restriction that no chair will be its own follow-up chair, and no two chairs will have the same follow-up chair. That is, the chef randomly chooses one arrangement out of all assignments satisfying the two conditions. The chef wonders, after a certain number of ringings of the bell, what the expected number of guests who will be back in their original chairs will be.

Input

Input will begin with an integer T, the number of test cases. Each test case consists of a single line with 2 integers N and R, the number of chairs and number of ringings, respectively.

Output

For each test case, output on a single line the expected number of guests who will be back in their original seats after exactly R ringings, rounded to 5 decimal places.

Sample Input

4
2 1
2 2
4 2
5 3

Sample Output

0.00000
2.00000
1.33333
1.36364

Constraints

T?300
2?N?50
1?R?1000000
Author: pieguy
Date Added: 10-11-2010
Time Limit: 1 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


Comments

The programs gets Runtime

burdakovd @ 28 Nov 2010 05:38 AM

The programs gets Runtime Error with really simple solution.

 

When I am using StreamTokenizer it seems to read n > 50: http://www.codechef.com/viewsolution/384780

When I am using Scanner it crashes when I just read input data (without any assertion or processing code): http://www.codechef.com/viewsolution/384782

Confirmed in C++, there's

triplem @ 28 Nov 2010 09:28 AM

Confirmed in C++, there's definitely something wrong with this problem: http://www.codechef.com/viewsolution/384826

Looks like the number of test cases was wrong, and it was just a lucky side effect of C++ that means anyone got accepted at all.

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