class Mo include Enumerable(Tuple(Int32, Int32, Int32)) def initialize(@n : Int32, @bucket_size : Int32) @bucket = Array(Array(Int32)).new((@n + @bucket_size - 1) // @bucket_size) { [] of Int32 } @qs = Array(Tuple(Int32, Int32)).new end def add_query(l : Int32, r : Int32) @bucket[l // @bucket_size] << @qs.size @qs << {l, r} end def build @bucket.size.times do |i| @bucket[i].sort_by! { |qi| @qs[qi][1] } if i % 2 != 0 @bucket[i].reverse! end end end def each @bucket.each do |b| b.each do |qi| yield ({@qs[qi][0], @qs[qi][1], qi}) end end end end class RBST(T) class Node(T) @left : Node(T) | Nil @right : Node(T) | Nil property :left, :right getter :val, :size def initialize(@val : T) @left = nil @right = nil @size = 1 end def height if left = @left lh = left.height else lh = 0 end if right = @right rh = right.height else rh = 0 end return {lh, rh}.max + 1 end def fix_size @size = 1 if left = @left @size += left.size end if right = @right @size += right.size end end def to_s(io : IO) to_s(io, 0) end def to_s(io : IO, level : Int32) if left = @left left.to_s(io, level + 1) end io << " " * level * 2 << @val << "\n" if right = @right right.to_s(io, level + 1) end end end @root : Node(T) | Nil def initialize @root = nil @rnd = Random.new end def insert(v : T) @root = insert(@root, v) end def insert(node : Node(T) | Nil, v : T) : Node(T) return Node(T).new(v) if !node if @rnd.rand(node.size + 1) == 0 return insert_root(node, v) end if v < node.val node.left = insert(node.left, v) else node.right = insert(node.right, v) end node.fix_size return node end def insert_root(node : Node(T) | Nil, v : T) : Node(T) return Node(T).new(v) if !node if v < node.val node.left = insert_root(node.left, v) return rotate_right(node) else node.right = insert_root(node.right, v) return rotate_left(node) end end def rotate_right(node : Node(T)) : Node(T) top = node.left.not_nil! mid = top.right top.right = node node.left = mid node.fix_size top.fix_size return top end def rotate_left(node : Node(T)) : Node(T) top = node.right.not_nil! mid = top.left top.left = node node.right = mid node.fix_size top.fix_size return top end def clear @root = nil end def remove(v : T) : Bool new_root, found = remove(@root, v) if found @root = new_root return true else return false end end def remove(node : Node(T) | Nil, v : T) : Tuple(Node(T) | Nil, Bool) return {nil, false} if !node if v == node.val return {meld(node.left, node.right), true} elsif v < node.val new_child, found = remove(node.left, v) if found node.left = new_child node.fix_size end else new_child, found = remove(node.right, v) if found node.right = new_child node.fix_size end end return {node, found} end def meld(left : Node(T) | Nil, right : Node(T) | Nil) : Node(T) | Nil return right if !left return left if !right if @rnd.rand(left.size + right.size) < left.size left.right = meld(left.right, right) left.fix_size return left else right.left = meld(left, right.left) right.fix_size return right end end def find(v : T) : Node(T) | Nil cur = @root while cur if v == cur.val return cur elsif v < cur.val cur = cur.left else cur = cur.right end end return nil end def nth(n : Int32) : T # 0-indexed cur = @root while cur ln = cur.left lc = ln ? ln.size : 0 if lc > n cur = cur.left elsif lc < n cur = cur.right n -= lc + 1 else break end end if cur return cur.val else raise Exception.new("cannot fine") end end def rank(v : T) : Int32 # 0-indexed, not count equivalent values cur = @root ret = 0 while cur if v <= cur.val cur = cur.left else if left = cur.left ret += left.size end ret += 1 cur = cur.right end end return ret end def lower(v : T) : T | Nil # largest value smaller than v cur = @root ret = nil while cur if cur.val < v ret = cur.val cur = cur.right else cur = cur.left end end return ret end def upper(v : T) : T | Nil # smallest value larger than v cur = @root ret = nil while cur if cur.val > v ret = cur.val cur = cur.left else cur = cur.right end end return ret end def size if root = @root return root.size else return 0 end end def height if root = @root root.height else 0 end end def to_s(io : IO) if root = @root root.to_s(io, 0) else io << "nil\n" end end end class BIT(T) # 1-indexed def initialize(size : Int) len = 1 while len < size len *= 2 end @v = Array(T).new(len + 1, T.zero) end def cumulative_sum(index : Int) ret = T.zero while index > 0 ret += @v[index] index &= index - 1 end ret end def sum(l : Int, r : Int) cumulative_sum(r) - cumulative_sum(l - 1) end def add(index : Int, val : T) while index < @v.size @v[index] += val index += (index & -index) end end def set(index : Int, val : T) old = sum(index, index) add(index, val - old) end end n, q = read_line.split.map(&.to_i) a = read_line.split.map(&.to_i64) b = read_line.split.map(&.to_i64) mo = Mo.new(n, 140) q.times do l, d, r, u = read_line.split.map(&.to_i) mo.add_query(l - 1, d - 1) mo.add_query(r, u) mo.add_query(l - 1, u) mo.add_query(r, d - 1) end mo.build ans = Array.new(q, 0i64) row = RBST(Int64).new col = RBST(Int64).new sum_row = BIT(Int64).new(100001) sum_col = BIT(Int64).new(100001) sum = 0i64 cl = 0 cr = 0 mo.each do |nl, nr, qi| # expand while cr < nr sum += b[cr] * col.rank(b[cr]) sum += sum_col.sum(b[cr], 100000) row.insert(b[cr]) sum_row.add(b[cr], b[cr]) cr += 1 end while cl < nl sum += a[cl] * row.rank(a[cl]) sum += sum_row.sum(a[cl], 100000) col.insert(a[cl]) sum_col.add(a[cl], a[cl]) cl += 1 end # shrink while cr > nr cr -= 1 sum -= b[cr] * col.rank(b[cr]) sum -= sum_col.sum(b[cr], 100000) row.remove(b[cr]) sum_row.add(b[cr], -b[cr]) end while cl > nl cl -= 1 sum -= a[cl] * row.rank(a[cl]) sum -= sum_row.sum(a[cl], 100000) col.remove(a[cl]) sum_col.add(a[cl], -a[cl]) end ans[qi // 4] += sum * (qi % 4 < 2 ? 1 : -1) end puts ans.join("\n")