Robot Movings

Problem code: MOVES

All submissions for this problem are available.

Given a square table sized NxN (3 ≤ N ≤ 5,000; rows and columns are indexed from 1) with a robot on it. The robot has a mission of moving from cell (1, 1) to cell (N, N) using only the directions "right" or "down". You are requested to find the number of different ways for the robot using exactly K turns (we define a "turn" as a right move followed immediately by a down move, or a down move followed immediately by a right move; 0 < K < 2N-2).

Input

There are several test cases (5,000 at most), each consisting of a single line containing two positive integers N, K.
The input is ended with N = K = 0.

Output

For each test case, output on a line an integer which is the result calculated. The number of ways may be very large, so compute the answer modulo 1,000,000,007.

Example

Input:
4 2
4 3
5 3
0 0

Output:
4
8
18

Explanation for the first sample test case: 4 ways are RRDDDR, RDDDRR, DRRRDD, DDRRRD ('R' or 'D' represents a right or down move respectively).

Author: anhdq
Tester: pieguy
Editorial http://discuss.codechef.com/problems/MOVES
Date Added: 22-08-2011
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, FORT, FS, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

A more simpler version of the

abhinav1 @ 20 Jun 2012 02:21 PM
A more simpler version of the problem is here.... http://projecteuler.net/problem=15 .. Well.....this one is a nice problem....took me at-least 3-4 hours to search a way for calculating nCr......

Though the problem costed me

k1e13 @ 13 Jun 2013 03:03 PM
Though the problem costed me a whole day ,it was worth it. ;) and yes, If anybody wants to learn some efficient way of calculating nCr or is struggling for ac just because of this problem then, here is the link: http://comments.gmane.org/gmane.comp.programming.algogeeks/29972 Hope it helps ;)

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