You are given an array $a$ consisting of $500000$ integers (numbered from $1$ to $500000$). Initially all elements of $a$ are zero.

You have to process two types of queries to this array:  $1$ $x$ $y$ — increase $a_x$ by $y$;  $2$ $x$ $y$ — compute $\sum\limits_{i \in R(x, y)} a_i$, where $R(x, y)$ is the set of all integers from $1$ to $500000$ which have remainder $y$ modulo $x$. 

Can you process all the queries?


-----Input-----

The first line contains one integer $q$ ($1 \le q \le 500000$) — the number of queries.

Then $q$ lines follow, each describing a query. The $i$-th line contains three integers $t_i$, $x_i$ and $y_i$ ($1 \le t_i \le 2$). If $t_i = 1$, then it is a query of the first type, $1 \le x_i \le 500000$, and $-1000 \le y_i \le 1000$. If $t_i = 2$, then it it a query of the second type, $1 \le x_i \le 500000$, and $0 \le y_i < x_i$.

It is guaranteed that there will be at least one query of type $2$.


-----Output-----

For each query of type $2$ print one integer — the answer to it.


-----Example-----
Input
5
1 3 4
2 3 0
2 4 3
1 4 -4
2 1 0

Output
4
4
0

Difficulty: HARD
Tags: Data structures

Implementation

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Skill types: Data structures

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Starter code:

Solutions:
import sys
from array import array
import typing as Tp

def input():
	return sys.stdin.buffer.readline().decode('utf-8')

def main():
	q = int(input())
	n = 500000
	m = 600
	a = array('i', [0]) * (n + 1)
	dp = [array('i', [0]) * (i + 1) for i in range(m + 1)]
	ans = []
	for _ in range(q):
		(t, x, y) = map(int, input().split())
		if t == 1:
			a[x] += y
			for i in range(1, m + 1):
				dp[i][x % i] += y
		elif x > m:
			ans.append(sum((a[i] for i in range(y, n + 1, x))))
		else:
			ans.append(dp[x][y])
	sys.stdout.buffer.write(('\n'.join(map(str, ans)) + '\n').encode('utf-8'))
main()


import sys
from sys import stdin, stdout
from collections import defaultdict
from collections import deque
import math
import copy
arr = [0] * 500001
K = 530
Q = int(sys.stdin.readline())
qus = sys.stdin.readlines()
small = [[0] * K for _ in range(K)]
ans = []
a = 0
for q in qus:
	(tag, idx, delta) = [int(x) for x in q.split()]
	if tag == 1:
		arr[idx] += delta
		for k in range(1, K + 1):
			small[k - 1][idx % k] += delta
	elif tag == 2:
		if idx <= K:
			ans.append(small[idx - 1][delta])
		else:
			res = 0
			for k in range(delta, 500001, idx):
				res += arr[k]
			ans.append(res)
print(*ans)


import sys
n = 500001
sqrt = int(0.75 * n ** 0.5)
data = [0] * n
ans = [[]]
for i in range(1, sqrt):
	ans.append([0] * i)
j = int(sys.stdin.readline())
qus = sys.stdin.readlines()
for qu in qus:
	q = [int(i) for i in qu.split()]
	if q[0] == 1:
		x = q[1]
		y = q[2]
		data[x] += y
		for i in range(1, sqrt):
			ans[i][x % i] += y
	else:
		if q[1] < sqrt:
			sys.stdout.write(str(ans[q[1]][q[2]]))
		else:
			sm = 0
			for i in range(q[2], n, q[1]):
				sm += data[i]
			sys.stdout.write(str(sm))
		sys.stdout.write('\n')


import sys
readline = sys.stdin.buffer.readline
ni = lambda : int(readline().rstrip())
nm = lambda : map(int, readline().split())

def solve():
	q = ni()
	n = 5 * 10 ** 5
	a = [0] * (n + 1)
	m = 710
	rem = [[0] * m for _ in range(m)]
	for _ in range(q):
		(t, x, y) = nm()
		if t == 1:
			a[x] += y
			for p in range(1, m):
				rem[p][x % p] += y
		elif x < m:
			print(rem[x][y])
		else:
			print(sum(a[y::x]))
solve()


import sys
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
ns = lambda : readline().rstrip()
ni = lambda : int(readline().rstrip())
nm = lambda : map(int, readline().split())
nl = lambda : list(map(int, readline().split()))
prn = lambda x: print(*x, sep='\n')

def solve():
	q = ni()
	n = 5 * 10 ** 5
	a = [0] * (n + 1)
	m = 720
	rem = [[0] * m for _ in range(m)]
	for _ in range(q):
		(t, x, y) = nm()
		if t == 1:
			a[x] += y
			for p in range(1, m):
				rem[p][x % p] += y
		elif x < m:
			print(rem[x][y])
		else:
			print(sum((a[i] for i in range(y, n + 1, x))))
solve()