J. Journey of the Particles
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

An experiment at the Large Hadron Collider is being set up to test phase properties of various different particles. There are $$$N$$$ filters arranged in a circle, where the $$$i$$$-th filter allows particles with a phase less than or equal to its limit $$$A_i$$$ to pass.

An experiment begins with the release of a particle at the position of the $$$i$$$-th filter, with an initial phase set to $$$A_i$$$. When passing through filter $$$i$$$, including the first one, the particle:

  • Is filtered out if the phase of the particle is greater than the limit $$$A_i$$$, ending the experiment.
  • Otherwise, the particle passes through the filter, increases its phase by $$$K$$$, and moves to the next filter on the right, the $$$(i \bmod N) + 1$$$-th filter.

We want to simulate the result of this experiment to compare with the results verified empirically. To achieve this, we need to create a vector $$$B_i$$$ of size $$$N$$$, where $$$B_i$$$ ($$$1 \leq B_i \leq N$$$) is the position of the filter that stopped the particle that started at position $$$i$$$.

Input

The first line contains two integers $$$N$$$ ($$$1 \leq N \leq 2 \cdot 10^5$$$) and $$$K$$$ ($$$1 \leq K \leq 10^9$$$). The second line contains $$$N$$$ integers $$$A_1, A_2, \ldots, A_N$$$ ($$$-10^9 \leq A_i \leq 10^9$$$).

Output

Print a line containing $$$N$$$ integers $$$B_1, B_2, \ldots, B_N$$$.

Examples
Input
4 1
4 3 1 2
Output
2 3 2 2
Input
5 5
-10 -5 0 5 10
Output
1 1 1 1 1
Input
6 2
12 4 5 9 2 3
Output
2 3 5 5 6 2