5593: DZY Loves FFT
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
B. DZY Loves FFT
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
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.
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.
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.
Examples
Input
3 1 1
Output
1 3 2
Input
5 4 2
Output
2 2 4 5 5
Input
5 4 3
Output
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].
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输出样例 复制