P11273 "Diligent-OI R1 C" DlgtRank

You are given a sequence $a_1\sim a_n$ of length $n$. Here, the **rank** of $a_i$ is defined as the number of elements in $a$ that are **strictly greater than** $a_i$, plus $1$. Now there are some operations to modify the elements in $a$. Before all operations, you are given a constant $k$ in advance. Before each operation, $a_i$ is defined to be **movable** if and only if, after **only adding $k$ to $a_i$ while keeping all other values unchanged**, the rank of $a_i$ does not change. Otherwise, $a_i$ is **not movable** in this operation. Then this operation is: add $k$ to all movable numbers in the sequence. It can be proven that after a certain number of operations, all values in $a$ will become movable, and once this state is reached for the first time, all subsequent operations will also stay in this state. In other words, no matter how many operations you perform, the number of times each value in $a$ is in the **not movable** state is finite. Now you are asked: after performing this operation sufficiently many times, how many times is each value in $a$ in the **not movable** state.

The first line contains two integers $n,k$. The next line contains $n$ integers $a_1\sim a_n$, representing the initial sequence $a$.

Output one line with $n$ integers. The $i$-th integer indicates how many times $a_i$ is in the **not movable** state during the operations.

#### Sample #1 Explanation Initially, $a_1=1,a_2=3,a_3=4$. After one operation, $a_1=2,a_2=3,a_3=5$. $a_2$ is not movable because if we only add $1$ to $a_2$, its rank would change from $2$ to $1$. After two operations, $a_1=2,a_2=4,a_3=6$. $a_1$ is not movable because if we only add $1$ to $a_1$, its rank would change from $3$ to $2$. After three operations, $a_1=3,a_2=5,a_3=7$. In this operation, all values are movable. It can be proven that no matter how many more operations you perform, the not movable state will never appear again. Therefore, during the process, $a_1$ is not movable once, $a_2$ is not movable once, and $a_3$ is never not movable. #### Constraints and Notes For $100\%$ of the testdata, $1\le n\le2\times10^5$, $1\le k,a_i\le10^9$. | Subtask ID | $n\le$ | Special Property | Score | | :----------: | :----------: | :----------: | :----------: | | $0$ | $1$ | ABC | $4$ | | $1$ | $100$ | C | $14$ | | $2$ | $100$ | None | $13$ | | $3$ | $3000$ | C | $18$ | | $4$ | $3000$ | None | $16$ | | $5$ | $2\times10^5$ | A | $6$ | | $6$ | $2\times10^5$ | BC | $8$ | | $7$ | $2\times10^5$ | C | $7$ | | $8$ | $2\times10^5$ | None | $14$ | Special property A: all $a_i$ are equal. Special property B: for any $i