Two players play a game with a deck of cards which contains $s$ suits with each suit containing $n$ cards numbered from $1$ to $n$.

Before the game starts, a set of cards (which may be empty) is picked from the deck and placed face-up on the table, with no overlap. These are called the visible cards.

The players then make moves in turn.
A move consists of choosing a card X from the rest of the deck and placing it face-up on top of a visible card Y, subject to the following restrictions:

• X and Y must be the same suit;
• the value of X must be larger than the value of Y.

The card X then covers the card Y and replaces Y as a visible card.
The player unable to make a valid move loses and play stops.

Let $C(n,s)$ be the number of different initial sets of cards for which the first player will lose given best play for both players.

For example, $C(3,2)=26$ and $C(13,4)\equiv 540318329(\mathrm{mod}1000000007)$.

Find $C({10}^7,{10}^7)$. Give your answer modulo $1000000007$.