Consider the following C++ code, it constructs n×n matrices A,B and vector V from matrix C=A×B which you need to calculate.

uint32_t n, i, j, d1, p1, r1, m1, d2, p2, m2, A[n][n], B[n][n];
uint64_t C[n][n], V[n];
//here you need to read n, p1, d1, r1, m1, p2, d2, r2, m2 from input.
for (i=0; i<n; ++i)
    for (j=0; j<n; ++j) {
        d1 = d1 * p1 + r1;
        d2 = d2 * p2 + r2;
        A[i][j] = d1 >> (32 - m1);
        B[i][j] = d2 >> (32 - m2);
    }
//here you need to calculate C=A*B
for (i=0; i<n; ++i) {
    V[i] = 0;
    for (j=0; j<n; ++j)
        V[i] ^= C[i][j];
}
//here you need to output V[0], V[1], ..., V[n-1], separated by spaces.

Input

You are given integers n, p1, d1, r1, m1, p2, d2, r2, m2, separated by spaces.

1≤n≤2048, 1≤m1,m2≤26, 0≤p1,d1,r1,p2,d2,r2<2³².

Output

You need to output V[0], ..., V[n-1], separated by spaces.

Example

Input:
4 1664525 0 1013904223 26 1664525 1 1013904223 26
Output:
3929555766216722 770418013451752 7738542081270672 4286515685761206

P.S.

There are 4 tests with n≈2048. My best solution time — ~3.2s (~0.8s per test) which is 20 times faster than time limit.

Also try the challenge MATRMUL, to get AC there your time here should be less than 14s for cubic algorithm and 16s for Strassen's.