code javascript: Check whether the given graph contains a path going through all vertices, one by one, in increasing order of their numbers.

Task description

You are given an undirected graph consisting of N vertices, numbered from $1$ to N$,$ and M edges.

The graph is described by two arrays, A and B$,$ both of length M$.$ A pair $($A$[$K$],$ B$[$K$]),$ for K from $0$ to M$-1,$ describes an edge between vertex A$[$K$]$ and vertex B$[$K$].$

Your task is to check whether the given graph contains a path from vertex $1$ to vertex N going through all of the vertices, one by one, in increasing order of their numbers. All connections on the path should be direct.

Write a function:

function solution$($N$,$ A$,$ B$)$;

that, given an integer N and two arrays A and B of M integers each, returns true if there exists a path from vertex $1$ to N going through all vertices, one by one, in increasing order, or false otherwise.

Examples:

$1.$ Given N $=4,$ A $=[1,2,4,4,3]$ and B $=[2,3,1,3,1],$ the function should return true. There is a path $(1->2->3->4)$ using edges $(1,2),(2,3)$ and $(4,3).$

$2.$ Given N $=4,$ A $=[1,2,1,3]$ and B $=[2,4,3,4],$ the function should return false. There is no path $(1->2->3->4),$ as there is no direct connection from vertex $2$ to vertex $3.$

$3.$ Given N $=6,$ A $=[2,4,5,3]$ and B $=[3,5,6,4],$ the function should return false. There is no direct connection from vertex $1$ to vertex $2.$

$4.$ Given N $=3,$ A $=[1,3]$ and B $=[2,2],$ the function should return true. There is a path $(1->2->3)$ using edges $(1,2)$ and $(3,2).$

Write an efficient algorithm for the following assumptions:

$$ N is an integer within the range $[2.\mathrm{.}100,000]$;

$$ M is an integer within the range $[0.\mathrm{.}100,000]$;

$$ all elements of arrays A and B are integers within the range $[1..$N$]$;

$$ there are no self$-$loops $($edges with A$[$K$]=$ B$[$K$])$ in the graph;

$$ there are no multiple edges between the same vertices.