There is an old country and the king fell in love with a devil. The devil always ask the king to do some crazy things. Although the king used to be wise and beloved by his people. Now he is just like a boy in love and can’t refuse any request from the devil. Also, this devil is looking like a very cute Loli.
Something bad actually happen. The devil makes this kingdom's people infected by a disease called lolicon. Lolicon will take away people's life in silence.
Although zp is died, his friend, ywan is not a lolicon. Y*wan is the only one in the country who is immune of lolicon, because he like the adult one so much.
As this country is going to hell, y*wan want to save this country from lolicon, so he starts his journey.
You heard about it and want to help ywan, but ywan questioned your IQ, and give you a question, so you should solve it to prove your IQ is high enough.
The problem is about counting. How many undirected graphs satisfied the following constraints?
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This graph is a complete graph of size n.
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Every edge has integer cost from 1 to L.
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The cost of the shortest path from 1 to n is k.
Can you solve it?
output the answer modulo 10^9+7
