Network Connectivity Check

You are given a network with n nodes and m edges. Each edge connects two distinct nodes. Your task is to determine whether there is a path between two specified nodes a and b in the network.

The network is undirected. Formally, given a graph \(G=(V,E)\) where \(V = \{1, 2, \dots, n\}\) and \(E\) consists of m edges, check if there exists a sequence of vertices \(v_1, v_2, \dots, v_k\) such that \(v_1 = a\), \(v_k = b\) and for every \(i=1, 2, \dots, k-1\), \((v_i, v_{i+1}) \in E\).

Output YES if a path exists, otherwise output NO.

inputFormat

The first line contains two integers \(n\) and \(m\) (the number of nodes and edges respectively).

The next \(m\) lines each contain two integers \(u\) and \(v\), representing an undirected edge between nodes \(u\) and \(v\).

The last line contains two integers \(a\) and \(b\): the two nodes to check connectivity.

All input is given through stdin.

outputFormat

Output a single line: YES if there exists a path between \(a\) and \(b\) in the network, and NO otherwise. Write the answer to stdout.

## sample

6 5
1 2
2 3
1 3
4 5
5 6
1 3

YES

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