Monica is a chef. Today, she wants to create dishes consisting of n ingredients. x grams of \(i^{\text{th}}\) ingredient has energy \(x^{a_i}\). Use \(0 ^ 0 = 1\). Two dishes are different if the amount of an ingredient differs in them. The energy of a dish is equal to product of energies of individual ingredients. Also, each dish is to be packed in a different container which can afford a weight of upto y grams.

She makes all distinct dishes with weight(= sum of amounts of ingredients) \( \le y\). Find the sum of energies of all the dishes made by her modulo \(10^9 + 7\). Note that an empty dish(one in which all ingredients have amount 0) is also valid.

Input:
The input consists of two lines:

• The first line contains two integers, n and y
• The second line contains n space separated integers, \(i^{\text{th}} \) of which is equal to \(a_i\)

Output:
Print only one line containing the sum of energies of all the dishes made by Monica modulo \(10^9 + 7\)

Constraints:

• \(1 \le n \le 10^5\)

• \(0 \le a_i \le 10^5\)

• \( \sum_{i=1}^{n} a_i \le 10^5 \)

• \(0 \le y \le 10^9\)