Contents
raw puzzle

Original Problem

Cities on a map are connected by a number of roads. The number of roads between each city is in an array and city \(0\) is the starting location. The number of roads from city \(0\) to city \(1\) is the first value in the array, from city \(1\) to city \(2\) is the second, and so on.

How many paths are there from city \(0\) to the last city in the list, modulo \(1234567\)?

Example

\(n=4\)
\(routes=[3,4,5]\)
There are \(3\) roads to city \(1\), \(4\) roads to city \(2\) and \(5\) roads to city \(3\). The total number of roads is \(3\times 4\times 5\mod 1234567 = 60\).

Note
Pass all the towns Ti for i=1 to n-1 in numerical order to reach Tn.

Function Description

Complete the connectingTowns function in the editor below.

connectingTowns has the following parameters:

Returns

Input Format
The first line contains an integer T, T test-cases follow.

Each test-case has 2 lines.
The first line contains an integer N (the number of towns).
The second line contains N - 1 space separated integers where the ith integer denotes the number of routes, Ni, from the town Ti to Ti+1

Constraints
1 <= T<=1000
2< N <=100
1 <= routes[i] <=1000

Sample Input

2
3
1 3
4
2 2 2

Sample Output

3
8

Explanation
Case 1: 1 route from T1 to T2, 3 routes from T2 to T3, hence only 3 routes.
Case 2: There are 2 routes from each city to the next, hence 2 * 2 * 2 = 8.

Solution

The solution was given already by the problem statement. We have to multiply all number of routes and since the number can get quite large, we are required to get the result modulo 1234567. To not rely on bigint, we make use of multiplicative rules of modulo and can solve the problem with

function connectingTowns(n, routes) {
  var p = 1;
  for (var r of routes) {
    p = (r * p) % 1234567;
  }
  return p % 1234567;
}