Sum of Consecutive Primes

You are given $m$ integers $n_1, n_2, \dots, n_m$.

A prime $p$ can be written as a "sum of $k$ consecutive primes" if there exist $k$ consecutive primes in the ascending list of all primes whose sum is exactly $p$.

Write a program that finds the smallest prime that can, at the same time, be written as a sum of $n_i$ consecutive primes for every given $n_i$.

For example, if $m = 2$, $n_1 = 3$, and $n_2 = 5$, the answer is $83$. It can be written as the sum of $3$ consecutive primes $23 + 29 + 31$ and also as the sum of $5$ consecutive primes $11 + 13 + 17 + 19 + 23$, and it is the smallest prime that satisfies both conditions.

The first line contains the number of test cases $T$.

Each test case consists of two lines. The first line contains an integer $m$ ($1 \le m \le 10$), and the second line contains $m$ space-separated integers $n_1, n_2, \dots, n_m$ ($1 \le n_i \le 10^4$).

In every test case the answer is guaranteed to be smaller than $10^7$.

For each test case, print Scenario i: on the first line, where $i$ is the $1$-based test case number, and print the answer prime on the second line.

Separate the outputs of consecutive test cases with a single blank line.