24067번 - KPart 서브태스크다국어

문제

Virgil has just set out to study the properties of arrays. Thus, he defines a $K$-array as any array $A$ of positive integers such that all length $K$ continuous subsequences of $A$ can be partitioned into two disjoint, potentially not continuous subsequences having equal sum. For example 1ドル,ドル 2ドル,ドル 1ドル,ドル 3ドル$ is a 3ドル$-array, since 1ドル,ドル 2ドル,ドル 1ドル$ can be partitioned into 1ドル,ドル 1ドル$ and 2ドル$ which both have sum 2ドル,ドル and 2ドル,ドル 1ドル,ドル 3ドル$ can be partitioned into 2ドル,ドル 1ドル$ and 3ドル$ which both have sum 3ドル$. It is not a 2ドル$-array, since 1ドル,ドル 2ドル$ cannot be partitioned into two potentially not continuous subsequences with equal sum. Likewise it is not a 4ドル$-array.

You are given $T$ arrays of positive integers. For each array $A$ Virgil wants to know all the values of $K$ for which $A$ is a $K$-array.

입력

The first line contains the integer $T$. The $T$ arrays follow. Each array is represented by two lines. The first line contains $N,ドル the length of the array. The second contains the elements of the array, separated by a single space.

출력

Output the answers for each array $A$ in order. For each array output only one line containing first the number of values of $K$ for which the given array is a $K$-array, and then those values of $K$ for which the array is a $K$-array, in increasing order.

제한

• 1ドル ≤ T ≤ 20$.
• Let $\sum{A}$ represent the sum of the values in any one array (not the sum of the values in all of the arrays). Then 1ドル ≤ \sum{A} ≤ 100,000円$.

서브태스크

힌트

The first array, the one of length 7ドル,ドル is a 4ドル$-array and 6ドル$-array, since each continuous subsequence of length 4ドル$ and 6ドル,ドル respectively, can be partitioned into two potentially not continuous subsequences with equal sum.

The second array, the one of length 6ドル,ドル is 3ドル$-array and 6ドル$-array, since each continuous subsequence of length 3ドル$ and the of length 6ドル$ can be partitioned into two potentially not continuous subsequences with equal sum.