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.\(//x is 64-bit variable; function getNextX() { x = (x * 37 + 10007) % 1000000007; return x; } function initAB() { for(i = 0; i \lt n; i = i + 1){ a[i] = i + 1; } for(i = 0; i \lt n; i = i + 1){ swap(a[i], a[getNextX() % (i + 1)]); } for(i = 0; i \lt n; i = i + 1){ if (i \lt d) b[i] = 1; else b[i] = 0; } for(i = 0; i \lt n; i = i + 1){ swap(b[i], b[getNextX() % (i + 1)]); } }\)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 \le d \le n \le 100000;0 \le x \le 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.

In the first sample, a is [1 3 2], b is [1 0 0], so c0=max(1 \cdot 1)=1, c1=max(1 \cdot 0,3 \cdot 1)=3, c2=max(1 \cdot 0,3 \cdot 0,2 \cdot 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].