You're given $$$n$$$ integers $$$a_1,a_2,\dots,a_n$$$, you need to count the number of ways to choose some of them (no duplicate) to make the sum equal to $$$S$$$. Print the answer in modulo $$$10^9+7$$$. How to solve this problem in polynomial time?

Note: The $$$n,S$$$ can be as large as $$$10^5$$$ so using single DP can't work. Using polygon $$$ln$$$ or $$$exp$$$ might work. But I don't know how to use them (I've just heard of it). Can anyone explain it?