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.