// 1-indiziert. Array t: [4*n][4*m]. Nur die _x-Varianten aufrufen.
// Laufzeit: build: O(n*m), update, sum: O(log(n)*log(m))
void build_y(int vx, int lx, int rx, int vy, int ly, int ry) {
  if (ly == ry) {
    if (lx == rx)vt[vx][vy] = a[lx][ly];
    else t[vx][vy] = t[vx*2][vy] + t[vx*2+1][vy];
  } else {
    int my = (ly + ry) / 2;
    build_y(vx, lx, rx, vy*2, ly, my);
    build_y(vx, lx, rx, vy*2+1, my+1, ry);
    t[vx][vy] = t[vx][vy*2] + t[vx][vy*2+1];
}}
 
void build_x(int vx = 1, int lx = 0, int rx = N-1) {
  if (lx != rx) {
    int mx = (lx + rx) / 2;
    build_x(vx*2, lx, mx);
    build_x(vx*2+1, mx+1, rx);
  }
  build_y(vx, lx, rx, 1, 0, m-1);
}

int sum_y(int vx, int vy, int tly, int try_, int ly, int ry) {
  if (ly > ry) return 0;
  if (ly == tly && try_ == ry) return t[vx][vy];
  int tmy = (tly + try_) / 2;
  return sum_y(vx, vy*2, tly, tmy, ly, min(ry,tmy))
    + sum_y(vx, vy*2+1, tmy+1, try_, max(ly,tmy+1), ry);
}

int sum_x(int vx=1, int tlx=0, int trx=n-1,int lx,int rx,int ly,int ry) {
  if (lx > rx) return 0;
  if (lx == tlx && trx == rx) return sum_y(vx, 1, 0, m-1, ly, ry);
  int tmx = (tlx + trx) / 2;
  return sum_x(vx*2, tlx, tmx, lx, min(rx,tmx), ly, ry)
    + sum_x(vx*2+1, tmx+1, trx, max(lx,tmx+1), rx, ly, ry);
}

void update_y(int vx, int lx, int rx, int vy, int ly, int ry,
    int x, int y, int new_val) {
  if (ly == ry) {
    if (lx == rx) t[vx][vy] = new_val;
    else t[vx][vy] = t[vx*2][vy] + t[vx*2+1][vy];
  } else {
    int my = (ly + ry) / 2;
    if (y <= my) update_y(vx, lx, rx, vy*2, ly, my, x, y, new_val);
    else update_y(vx, lx, rx, vy*2+1, my+1, ry, x, y, new_val);
    t[vx][vy] = t[vx][vy*2] + t[vx][vy*2+1];
}}
 
void update_x(int vx=1, int lx=0, int rx=n-1, int x, int y, int new_val) {
  if (lx != rx) {
    int mx = (lx + rx) / 2;
    if (x <= mx) update_x(vx*2, lx, mx, x, y, new_val);
    else update_x(vx*2+1, mx+1, rx, x, y, new_val);
  }
  update_y(vx, lx, rx, 1, 0, m-1, x, y, new_val);
}