You are given a single integer N denoting the number of elements in an array A and also the first element of the array i.e. A[1]. The rest of the elements are generated such that absolute difference between adjacent elements of the array is equal to 1.

mathematically,
for all 1 < i ≤ N, abs(A[i] - A[i-1])  = 1.

You are now given an integer K. Your task is to print the K^th lexicographical array that can be generated using the above method. K will be given such that the K^th lexicographical array exists.

Note that the generated numbers can be negative too.

INPUT FORMAT

Only line of input contains three space separated integers N, K, A[1] denoting the size of array, the rank of the lexicographical array we want to find and the first element of the array.

OUTPUT FORMAT

Print N space separated integers of the Kth lexicographical array.

CONSTRAINTS

• 1 ≤ N ≤ 10⁵
• 1 ≤ K ≤ 10¹⁸
• -10⁹ ≤ A[1] ≤ 10⁹