Fraction solve() {
Fraction zero = Fraction(0);
while (true) {
// pivot column
int c=-1;
Fraction best_col = zero;
for (int i=0;i<m;i++) {
if (t[n][i].compareTo(best_col)>0) {
c=i;
best_col = t[n][i];
}
}
if (c==-1) break;
// pivot row
int r=-1;
Fraction best_ratio = Fraction(-1);
for (int i=0;i<n;i++) {
if (t[i][c].compareTo(zero)==0) continue;
Fraction ratio = t[i][m].div(t[i][c]);
if (ratio.compareTo(zero)<0) continue;
if (ratio.compareTo(zero)==0 && t[i][c].compareTo(zero)<0) continue;
if (best_ratio.compareTo(zero)<0 || ratio.compareTo(best_ratio)<0) {
r=i; best_ratio=ratio;
}
}
Fraction pivot = t[r][c];
Fraction inv_pivot = pivot.inv();
Fraction neg_inv_pivot = inv_pivot.neg();
// update pivot
t[r][c] = inv_pivot;
// update row
for (int j=0;j<=m;j++) if (j!=c) {
t[r][j] = t[r][j].mul(inv_pivot);
}
// list of other rows and columns to update
nr=0; nc=0;
for (int i=0;i<=n;i++) if (i!=r) {
if (t[i][c].compareTo(zero)!=0) rows[nr++]=i;
}
for (int j=0;j<=m;j++) if (j!=c) {
if (t[r][j].compareTo(zero)!=0) cols[nc++]=j;
}
// update other
for (int i=0;i<nr;i++) {
int y=rows[i];
for (int j=0;j<nc;j++) {
int x=cols[j];
t[y][x] = t[y][x].sub(t[r][x].mul(t[y][c]));
}
}
// update column
for (int i=0;i<=n;i++) if (i!=r) {
t[i][c] = t[i][c].mul(neg_inv_pivot);
}
// update labels
int tmp = labelC[c];
labelC[c] = labelR[r];
labelR[r] = tmp;
}
return t[n][m].neg();
}
