$A={a_1, a_2, \cdots, a_n }$ is a set containing $n$ natural numbers (non negative integers) (according to the definition of the set, the number of $n$ is different in two), and the maximum value is less than a given positive integer $k$.↵
We needs to perform several rounds of merging operations on the numbers in the set $A$ until there is only one number left in $A$.↵
The process of each round of consolidation is as follows:↵
↵
1. Select number pairs $(x,y)$:↵
↵
- Select the two closest numbers $x $and $y $from $A $, that is, $|x-y|$ is the smallest of all pairs;↵
- If multiple number pairs meet the conditions, further select the one with the smallest $(x+y)$;↵
- Considering the difference between two numbers in $A$ , the unique number pair $(x,y)$ can be selected according to the above requirements (that is, $| x - y |$ is the first keyword, and $(x+y)$ is the second keyword).↵
↵
2. Merge $x$ and $y$ into $z$: $z=(x+y)mod k$↵
↵
- Specifically, first delete $x$ and $y$ from the set $A$; If the set $A$ does not contain $z$, add $z$back to the set $A$.This ensures that the natural numbers in $A$ are always different and less than $k$.↵
↵
↵
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We need to know the total number of merge operations and the remaining number in $A$ after all merge operations are completed.↵
All the data satisfies $ n\le10^5$ , $k \le 10^8$ , $a_i（1 \le i \le n , 0 \leq a_i \le k ）$ and all $a_i$ is different.
We needs to perform several rounds of merging operations on the numbers in the set $A$ until there is only one number left in $A$.↵
The process of each round of consolidation is as follows:↵
↵
1. Select number pairs $(x,y)$:↵
↵
- Select the two closest numbers $x $and $y $from $A $, that is, $|x-y|$ is the smallest of all pairs;↵
- If multiple number pairs meet the conditions, further select the one with the smallest $(x+y)$;↵
- Considering the difference between two numbers in $A$ , the unique number pair $(x,y)$ can be selected according to the above requirements (that is, $| x - y |$ is the first keyword, and $(x+y)$ is the second keyword).↵
↵
2. Merge $x$ and $y$ into $z$: $z=(x+y)mod k$↵
↵
- Specifically, first delete $x$ and $y$ from the set $A$; If the set $A$ does not contain $z$, add $z$back to the set $A$.This ensures that the natural numbers in $A$ are always different and less than $k$.↵
↵
↵
↵
We need to know the total number of merge operations and the remaining number in $A$ after all merge operations are completed.↵
All the data satisfies $ n\le10^5$ , $k \le 10^8$ , $a_i（1 \le i \le n , 0 \leq a_i \le k ）$ and all $a_i$ is different.
