Problem:
Range Sum Query

Write a program which manipulates a sequence A = {a1, a2, . . . , an} with the following operations:

add(i, x): add x to ai.

getSum(s, t): print the sum of as, as+1,...,at.

Note that the initial values of ai (i = 1, 2, . . . , n) are 0.

Input

n q
com1 x1 y1
com2 x2 y2
...
comq xq yq

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes add(xi, yi) and '1' denotes getSum(xi, yi).

Output

For each getSum operation, print the sum in a line.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 1 ≤ xi ≤ n, 0 ≤ yi ≤ 1000.

If comi is 1, then 1 ≤ xi ≤ n, 1 ≤ yi ≤ n.

Sample Input 1

3 5
0 1 1
0 2 2
0 3 3
1 1 2
1 2 2

Sample Output 1

3
2

Solution in Ruby (judge verdict: Accepted)

def init
  x = 1
  while x < $n
    x <<= 1
  end
  $n = x
  $arr = Array.new(2*x-1, 0)
end

def update(i, x)
  i += $n - 1
  $arr[i] += x
  while i > 0
    i = (i - 1) / 2
    $arr[i] = $arr[i*2+1] + $arr[i*2+2]
  end
end

def query(a,b,k,l,r)
  if r <= a || b <= l then return 0
  end
  if a <= l && r <= b then return $arr[k]
  else
    vl = query(a, b, k*2+1, l, (l+r) / 2)
    vr = query(a, b, k*2+2, (l+r) / 2, r)
    return vl + vr
  end
end

$n, q = gets.split.map(&:to_i)
init
q.times do
  cmd, x, y = gets.split.map(&:to_i)
  x -= 1
  if cmd == 0 then update(x, y)
  else 
    y -= 1
    puts query(x, y+1, 0, 0, $n)
  end
end