Chess Pushing Game
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Dave is playing a game with three pawns on a long board. The board can be seen as an (semi-)infinitely long sequence of grid squares numbered starting from 0 with width 3. Thus, the squares on the board can be referred to using (i,j) where i >= 0 and j = 0, 1 or 2. For this problem, the distance between two pawns is the distance along the first coordinate. For example, distance between pawns at (0,2) and (10,0) is 10.
The pawns are numbered 0, 1 and 2. Pawn j starts off at square (0, j) initially. In one move, a pawn can move one square to the right (increasing first coordinate, while second coordinate remains same). For example, a pawn can move from (4, 2) to (5,2). Another restriction is that if p < q, then pawn q can never be to the right(higher first coordinate) of pawn p. Yet another restriction is that at any point of time, pawns p and p+1 (for p=0 or p=1) should not be separated by a distance more than D.
At the end of K moves, all the pawns should end up at the same first coordinate. Dave wants to know how many ways there are to complete this game. Help him!
The first and only line contains two integers D, K (0 ≤ D ≤ 7; 0 ≤ K ≤ 109).
Output an only integer which is the result calculated, by modulo of 1,000,000,007.
Input: 1 3 Output: 1 Input: 2 6 Output: 5
|Tags||anhdq, jan11, medium|
|Time Limit:||0.439825 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, PERL6, TEXT, PYP3, CLOJ, FS|
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