How many sequences | CodeChef

How many sequences

Problem code: SEQCOUNT

All submissions for this problem are available.

Read problems statements in Mandarin Chinese and Russian.

Consider the sequence of K natural numbers: a1, a2, ..., aK. Tooru thinks that this sequence is nice if and only if:

  • a1+a2+...+aK = N
  • a1 < a2 < ... < aK
  • ai+1 - ai <= D for every natural i, smaller than K
  • a1 <= D



You are given N, K and D. Please, count the number of nice sequences for her. This number can be huge, so we ask you to output it modulo 109+7.

Input

The first and only line of the input consists of the integers N, K and D, separated by a single space.

Output

Output the number of nice sequences on the first line of the output modulo 109+7.

Example

Input:
10 4 1

Output:
1

Explanation

The only suitable sequence is (1, 2, 3, 4).

Scoring

1 <= N, K, D <= 10 : 17 points.

1 <= N, K, D <= 400 : 23 points.
1 <= N, K, D <= 2000 : 20 points.

1 <= N, K, D <= 105 : 40 points.

Author: 6★xcwgf666
Tester:
Editorial http://discuss.codechef.com/problems/SEQCOUNT
Tags dynamic-programming, easy-medium, ltime10, xcwgf666
Date Added: 7-03-2014
Time Limit: 1 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, TCL, PERL6, TEXT, PYP3, CLOJ, FS


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