Description

An army of ants walk on a horizontal pole of length l cm, each with a constant speed of 1 cm/s. When a walking ant reaches an end of the pole, it immediatelly falls off it. When two ants meet they turn back and start walking in opposite directions. We know the original positions of ants on the pole, unfortunately, we do not know the directions in which the ants are walking. Your task is to compute the earliest and the latest possible times needed for all ants to fall off the pole.

Input

The first line of input contains one integer giving the number of cases that follow. The data for each case start with two integer numbers: the length of the pole (in cm) and n, the number of ants residing on the pole. These two numbers are followed by n integers giving the position of each ant on the pole as the distance measured from the left end of the pole, in no particular order. All input integers are not bigger than 1000000 and they are separated by whitespace.

Output

For each case of input, output two numbers separated by a single space. The first number is the earliest possible time when all ants fall off the pole (if the directions of their walks are chosen appropriately) and the second number is the latest possible such time.

Sample Input

210 32 6 7214 711 12 7 13 176 23 191

Sample Output

4 838 207 大意是说杆上有蚂蚁，只知道离左边的位置，不知道方向。给定杆长，问最短和最长落下的时间。 代码如下：

1 #include 
     
       2 #include 
      
        3 #include 
       
         4 #include 
        
          5 using namespace std; 6  7 int n; 8 int main(int argc, char const *argv[]) 9 {10     while(scanf("%d",&n) != EOF) {11         while(n--) {12             int len, m;13             int min0 = -1, max0 = -1;14             scanf("%d %d",&len,&m);15             while(m--) {16                 int p;17                 scanf("%d",&p);18                 min0 = max(min0, min(p, len-p));19                 max0 = max(max0,max(p,len-p));20             }21             printf("%d %d\n",min0, max0);22 23         }24     }25 }