1500 - Nice Prefixes
Time Limit : 2 Second
Memory Limit : 256 MB
Submission: 32
Solved: 5
- Description
- Consider strings formed from characters from an alphabet of size K. For example, if K = 4, our alphabet might be {a,b,c,d}, and an example string is bbcac.
For a string S, define count(S, k) to be the number of occurrences of the symbol k in S. For example, count(bbcac, b) = 2 and count(bbcac, a) = 1.
A prefix of a string S is any string obtained from S by deleting some (possibly none) of the trailing characters of S. For example, the prefixes of acb are the empty string, a, ac, and acb.
A string S has "nice prefixes" if for every prefix P of S and for every two characters k1 and k2 in the alphabet, |count(P, k1) - count(P, k2)| <= 2. For example, bbcac has nice prefixes, but abbbc does not because count(abbb, b) = 3 and count(abbb, c) = 0.
Count the number of strings of length L on an alphabet of size K that have nice prefixes. This number can be large, so print its remainder when divided by 1000000007.
- Input
- The input is a single line containing the two integers L and K, separated by spaces, with 1 <= L <= 1018 and 1 <= K <= 50.
- Output
- Output a single line containing the number of strings of length L on an alphabet of size K that have nice prefixes, modulo 1000000007.
- sample input
-
4 2
- sample output
-
12
- hint
- source
- waterloo 13 June, 2009