B. DZY Loves FFTtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputDZY 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, andWe can calculate c fast using Fast Fourier Transformation.DZY made a little change on this formula. NowTo 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.InputThe 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.OutputOutput n lines, the i-th line should contain an integer ci - 1.ExamplesInput3 1 1Output132Input5 4 2Output22455Input5 4 3Output55554NoteIn 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].
Input3 1 1
Output132
['probabilities', '*2300']