Measure trunk

We'll call a trunk of a rooted tree the set of nodes in the tree that are at a distance at most $x$ from the root. The distance is the sum of the lengths of edges on the path between nodes.

Imagine an infinite rooted tree where each node has exactly $n$ sons, at that for each node, the distance between it and its $i$-th left child equals to $d_i$. The task is to calculate the size of the trunk of such tree.

As the answer can be rather large, find it modulo $10^9+7$.

Input

The first line contains two space-separated integers $n$ and $x(1\le n\le 10^5,0\le x\le 10^9)$ — the number of children of each node and the distance from the root within the range of which you need to count the nodes.

The next line contains $n$ space-separated integers $d_i(1\le d_i\le 100)$ — the length of the edge that connects each node with its $i$-th child.

Output

Print a single number — the number of vertices in the tree at distance from the root equal to at most $x$.

Examples

Pictures to the sample (the yellow color marks the nodes the distance to which is at most three)