## Thursday, November 24, 2016

### Connecting Towns

Gandalf is travelling from Rohan to Rivendell to meet Frodo but there is no direct route from Rohan (T1) to Rivendell (Tn).
But there are towns T2,T3,T4...Tn-1 such that there are N1 routes from Town T1 to T2, and in general, Ni routes from Tito Ti+1 for i=1 to n-1 and 0 routes for any other Ti to Tj for j ≠ i+1
Find the total number of routes Gandalf can take to reach Rivendell from Rohan.
Note
Gandalf has to pass all the towns Ti for i=1 to n-1 in numerical order to reach Tn.
For each Ti , Ti+1 there are only Ni distinct routes Gandalf can take.
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
Output Format
Total number of routes from T1 to Tn modulo 1234567
http://en.wikipedia.org/wiki/Modular_arithmetic
Constraints
1 <= T<=1000
2< N <=100
1 <= Ni <=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, at each city, Gandalf has 2 choices to make, hence 2 * 2 * 2 = 8.