B'There are n benches near the Main Walkway in Summer Infomatics School. These benches are numbered by integers from 1 to n in order they follow. Also there are m cookie sellers near the Walkway. The i -th ( 1 <= i <= m ) cookie sellers is located near the s_i -th bench. Petya is standing in the beginning of the Walkway. He will pass near all benches starting from the 1 -st bench and ending with the n -th bench. Petya passes the distance between two consecutive benches in 1 minute. He has a knapsack with an infinite amount of cookies. Petya is going to eat cookies from his knapsack and buy them from cookie sellers during the walk. Petya eats cookies only near the benches according to the following rule: he will eat the cookie near the i -th ( 1 <= i <= n ) bench if and only if at least one of the following conditions holds: You may assume that Petya eats cookies instantly. Petya will not eat two or more cookies near the same bench. You want to minimize the number of cookies Petya will eat during his walk. In order to do this, you will ask the administration of the Summer Informatics School to remove exactly one cookie seller from the Walkway before Petya starts his walk. Please determine the minimum possible number of cookies Petya can eat after removing exactly one cookie seller. Also determine the number of cookie sellers, such that if you remove one of them, Petya will eat the minimum possible number of cookies. The first line contains a single integer t ( 1 <= t <= 10^3 ) -- the number of test cases. The first line of each test case contains three integers n , m and d ( 2 <= d <= n <= 10^9 , 2 <= m <= min(10^{5}, n) ) -- the number of benches, the number of cookie sellers and the value of parameter d from the statement, respectively. The second line of each test case contains m integers s_1, s_2, ldots, s_m ( 1 <= s_i '...