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void normalLine(int n, int line, ll p) {
ll factor = multInv(mat[line][line], p);
for (int i = 0; i <= n; i++) {
mat[line][i] *= factor;
mat[line][i] %= p;
}}
void takeAll(int n, int line, ll p) {
for (int i = 0; i < n; i++) {
if (i == line) continue;
ll diff = mat[i][line];
for (int j = 0; j <= n; j++) {
mat[i][j] -= (diff * mat[line][j]) % p;
mat[i][j] %= p;
if (mat[i][j] < 0) mat[i][j] += p;
}}}
void gauss(int n, ll p) { // nx(n+1)-Matrix, Körper F_p.
for (int line = 0; line < n; line++) {
int swappee = line;
while (swappee < n && mat[swappee][line] == 0) swappee++;
if (swappee == n) continue;
swap(mat[line], mat[swappee]);
normalLine(n, line, p);
takeAll(n, line, p);
// für Eindeutigkeit, Existenz etc. siehe LGS
}}
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