You are given $$N$$ nodes with the following information:

• The nodes are connected by $$M$$ bidirectional edges.
• Each node has a value \(V_i\) associated with it.
• A node is called a weak node if the connections between some other nodes are broken when that node is deleted and any alternate connections are not present.

Write a program to tell the number of subsets from all the possible subsets of weak nodes, which on getting their values multiplied gives a number which is divisible by all primes less than \(25\).

Since the answer can be large, print the answer Modulo \(10^9+7\).

Input format

• First line: Two space-separated integers $$N$$ and $$M$$
• Second line: $$N$$ space-separated integers denoting the values of the nodes
• Next $$M$$ lines: Two space-separated integers $$U$$ and $$V$$ denoting an edge between $$U$$ and $$V$$

Output format

Print the required answer Modulo \(10^9+7\).

Constraints

\(1 \le N, M \le 5 \times 10^4\)
\(1 \le U, V \le N\)
\(1 \le V \le 10^9\)