Hongjun likes FFT

Hongjun likes the fast Fourier transform (FFT) and uses it often.

FFT is an algorithm for computing a convolution. Given sequences $a$ and $b$ of length $n$, indexed from element 0 to element $n-1$, FFT quickly produces the sequence $c$ defined below.

$c_i = \sum_{j=0}^{i} a_j b_{i-j}$

Hongjun replaced the sum in this formula with a maximum.

$c_i = \max_{0 \le j \le i} a_j b_{i-j}$

To keep the computation easy, Hongjun only considers the case where $a$ holds each number from $1$ to $n$ exactly once and every element of $b$ is 0 or 1. If every product is 0, then $c_i$ is 0. Write a program that computes the sequence $c$ once $a$ and $b$ are fixed.

Hongjun is lazy, so he does not want to list the elements of $a$ and $b$ one by one. He gives only three integers $n$, $d$, $x$ and wants you to build both sequences yourself with the pseudocode below. % is the remainder operator and swap() exchanges two values. Following the pseudocode, $b$ contains exactly $d$ ones.

//x is 64-bit variable;
function getNextX() {
    x = (x * 37 + 10007) % 1000000007;
    return x;
}
function initAB() {
    for(i = 0; i < n; i = i + 1){
        a[i] = i + 1;
    }
    for(i = 0; i < n; i = i + 1){
        swap(a[i], a[getNextX() % (i + 1)]);
    }
    for(i = 0; i < n; i = i + 1){
        if (i < d)
            b[i] = 1;
        else
            b[i] = 0;
    }
    for(i = 0; i < n; i = i + 1){
        swap(b[i], b[getNextX() % (i + 1)]);
    }
}

The first line contains three integers $n$, $d$, $x$ separated by spaces. ($1 \le d \le n \le 100{,}000$, $0 \le x \le 1{,}000{,}000{,}006$)

Print the elements of the sequence $c$, from element 0 to element $n-1$, on one line separated by spaces.