[Solution] Make A and B equal CodeChef Solution

Problem

Chef is given two arrays $A$ and $B$ of length $N$ each.

In one operation Chef can choose one element of $A$ and one element of $B$ and increase them by $1$.

More formally: Chef can pick two integers $i, j$ $(1\le i, j \le N)$ and increment $A_i$ and $B_j$ by $1$.

Determine the minimum number of operations required to make $A$ and $B$ equal.

Output $-1$ if it is not possible to make $A$ and $B$ equal.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of multiple lines of input.
• The first line of each test case contains a single integer $N$ - denoting the length of arrays $A$ and $B$.
• The second line of each test case contains $N$ space separated integers $A_1, A_2, A_3, \dots A_N$ - denoting the array $A$.
• The third line of each test case contains $N$ space separated integers $B_1, B_2, B_3, \dots B_N$ - denoting the array $B$.

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Output Format

For each test case, output the minimum number of operations to make $A$ and $B$ equal or $-1$ if they cannot be made equal.

Explanation:

Test case $1$: We can choose $i = 1$ and $j = 2$ and increment $A_i$ and $B_j$ by $1$. Thus, both arrays become $[2, 2]$ and are equal. We require only $1$ operation to make these arrays equal. It can be proven that the arrays cannot be made equal in less than one operation.

Test case $2$: Both the arrays cannot be made equal using any number of operations.

Test case $3$: We perform $2$ operations as follows:

• Choose $i = 1, j = 3$: The arrays become $A = [5, 6, 8]$ and $B = [5, 7, 7]$.
• Choose $i = 2, j = 3$: The arrays become $A = [5, 7, 8]$ and $B = [5, 7, 8]$.

Thus, both arrays can be made equal using $2$ operations.