DZY Loves FFT
Description
DZY loves Fast Fourier Transformation, and he enjoys using it.
Fast Fourier Transformation is an algorithm used to calculate convolution. Specifically, if a, b and c are sequences with length n, which are indexed from 0 to n - 1, and
We can calculate c fast using Fast Fourier Transformation.
DZY made a little change on this formula. Now
To make things easier, a is a permutation of integers from 1 to n, and b is a sequence only containing 0 and 1. Given a and b, DZY needs your help to calculate c.
Because he is naughty, DZY provides a special way to get a and b. What you need is only three integers n, d, x. After getting them, use the code below to generate a and b.
//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)]);
}
}
Operation x % y denotes remainder after division x by y. Function swap(x, y) swaps two values x and y.
The only line of input contains three space-separated integers n, d, x (1 ≤ d ≤ n ≤ 100000; 0 ≤ x ≤ 1000000006). Because DZY is naughty, x can't be equal to 27777500.
Output n lines, the i-th line should contain an integer ci - 1.
Input
The only line of input contains three space-separated integers n, d, x (1 ≤ d ≤ n ≤ 100000; 0 ≤ x ≤ 1000000006). Because DZY is naughty, x can't be equal to 27777500.
Output
Output n lines, the i-th line should contain an integer ci - 1.
Samples
3 1 1
1
3
2
5 4 2
2
2
4
5
5
5 4 3
5
5
5
5
4
Note
In the first sample, a is [1 3 2], b is [1 0 0], so c0 = max(1·1) = 1, c1 = max(1·0, 3·1) = 3, c2 = max(1·0, 3·0, 2·1) = 2.
In the second sample, a is [2 1 4 5 3], b is [1 1 1 0 1].
In the third sample, a is [5 2 1 4 3], b is [1 1 1 1 0].