You've got an array a , consisting of n integers. The array elements are indexed from 1 to n . Let's determine a two step operation like that: First we build by the array a an array s of partial sums, consisting of n elements. Element number i ( 1 ≤ i ≤ n ) of array s equals . The operation x mod y means that we take the remainder of the division of number x by number y . Then we write the contents of the array s to the array a . Element number i ( 1 ≤ i ≤ n ) of the array s becomes the i -th element of the array a ( a i = s i ). You task is to find array a after exactly k described operations are applied. The first line contains two space-separated integers n and k ( 1 ≤ n ≤ 2000 , 0 ≤ k ≤ 10 9 ). The next line contains n space-separated integers a 1 , a 2 , ..., a n — elements of the array a ( 0 ≤ a i ≤ 10 9 ). Print n integers — elements of the array a after the operations are applied to it. Print the elements in the order of increasing of their indexes in the array a . Separate the printed numbers by spaces.