Chef is going to organize a hill jumping competition and he is going to be one of the judges in it. In this competition there are N hills in a row, and the initial height of i-th hill is Ai. Participants are required to demonstrate their jumping skills by doing what the judges tell them.
Judges will give each participant a card which has two numbers, i and k, which means that the participant should start at the i-th hill and jump k times, where one jump should be from the current hill to the nearest hill to the right which is strictly higher (in height) than the current one. If there is no such hill or its distance (i.e. difference between their indices)  is more than 100 then the participant should remain in his current hill.
Please help Chef by creating a program to use it during the competitions. It should read the initial heights of the hill and should support two kinds of operations:
Type 1: Given a two numbers: i and k, your program should output the index of the hill the participant is expected to finish if he starts from the i-th hill (as explained above).
Type 2: Given three numbers: L, R, X, the heights of all the hills between L and R, both end points inclusive, should be increased by X (if X is negative then their height is decreased).

-----Input-----
- First line contains two integers N and Q, denoting the number of hills and number of operations respectively.
- Second line contains N space-separated integers A1, A2, ..., AN denoting the initial heights of the hills.
- Each of the next Q lines describes an operation. If the first integer is equal to 1, it means that the operation is of Type 1, and it will be followed by two integers i and k. Otherwise the first number will be equal to 2, and it means that the operation is of Type 2, and so it will be followed by three integers L, R and X.

-----Output-----
For each operation of Type 1, output the index of the hill in which the participant will finish.

-----Constraints-----
- 1 ≤ N, Q ≤ 100,000
- 1 ≤ Ai ≤ 1,000,000
- 1 ≤ L ≤ R ≤ N
- -1,000,000 ≤ X ≤ 1,000,000
- 1 ≤ i, k ≤ N

-----Subtasks-----
- Subtask 1 (20 points) : 1 ≤ N, Q ≤ 1,000 
- Subtask 2 (80 points) : Original constraints

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

Output:
3
4

-----Explanation-----
The initial heights are (1, 2, 3, 4, 5). The first operation is of Type 1 and starts from Hill 1 and wants to jump twice. The first jump will be to Hill 2, and the second jump will be to Hill 3. Hence the output for this is 3.
The second operation changes the heights to (1, 2, 2, 3, 5).
The last operation starts from Hill 1. The first jump is to Hill 2. But the next jump will skip Hill 3 (because it's height is not strictly greater than the current hill's height), and will go to Hill 4. Hence the output is 4.

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
(n, q) = list(map(int, input().split()))
final = []
height = list(map(int, input().split()))
for k in range(0, q):
	b = input().split()
	if int(b[0]) == 1:
		step = int(b[1]) - 1
		for k in range(0, int(b[2])):
			temp = 0
			j = 1
			while j in range(1, 101) and temp == 0 and (step + j < n):
				if height[step + j] > height[step]:
					step = step + j
					temp = 1
				j += 1
		final.append(step + 1)
	elif int(b[0]) == 2:
		for k in range(int(b[1]) - 1, int(b[2])):
			height[k] = height[k] + int(b[3])
for l in range(0, len(final)):
	print(final[l])


def find_pos(arr, n, p, c):
	i = p
	i1 = p
	while i <= n and c > 0:
		if arr[i1] < arr[i]:
			if i - i1 > 100:
				return i1
			(c, i1) = (c - 1, i)
		i += 1
	return i1
(n, q) = list(map(int, input().split()))
arr = [0] + list(map(int, input().split()))
for a0 in range(1, q + 1):
	temp = list(map(int, input().split()))
	if temp[0] == 1:
		(p, c) = (temp[1], temp[2])
		print(find_pos(arr, n, p, c))
	else:
		(l, r, val) = (temp[1], temp[2], temp[3])
		for i in range(l, r + 1):
			arr[i] += val


(n, q) = list(map(int, input().split()))
hill = list(map(int, input().split()))

def get_answer_type_1(i, k):
	for ind in range(k):
		curr_elem = hill[i]
		for ind_sub in range(i, i + 101):
			try:
				this_elem = hill[ind_sub]
			except:
				break
			if this_elem > curr_elem:
				i = ind_sub
				break
	return i + 1

def get_answer_type_2(l, r, x):
	for ind in range(l, r + 1):
		hill[ind] += x
for i in range(q):
	query = input().split()
	if query[0] == '1':
		(i, k) = list(map(int, query[1:]))
		i -= 1
		print(get_answer_type_1(i, k))
	else:
		(l, r, x) = list(map(int, query[1:]))
		l -= 1
		r -= 1
		get_answer_type_2(l, r, x)


def find_final_posi(l1, cp, jumps):
	count = 0
	i = cp
	while i in range(cp, cp + 101):
		if (count == jumps) | (i >= len(l1)):
			return cp
		elif l1[cp] < l1[i]:
			cp = i
			i += 1
			count += 1
		else:
			i += 1
	return cp
[n, q] = [int(x) for x in input().split()]
hillht = [-1]
hillht.extend([int(x) for x in input().split()])
for j in range(q):
	oper = [int(x) for x in input().split()]
	if oper[0] == 2:
		for x in range(oper[1], oper[2] + 1):
			hillht[x] += oper[3]
	else:
		print(find_final_posi(hillht, oper[1], oper[2]))


(n, q) = list(map(int, input().split()))
l = list(map(int, input().split()))
for i in range(q):
	s = list(map(int, input().split()))
	if s[0] == 1:
		ind = s[1] - 1
		jump = s[2]
		j = ind + 1
		val = l[ind]
		while True:
			if j >= len(l):
				break
			if l[j] > val and j - ind <= 100 and (jump > 0):
				val = l[j]
				jump -= 1
				ind = j
			if j - ind > 100:
				break
			if jump <= 0:
				break
			j += 1
		print(ind + 1)
	else:
		left = s[1] - 1
		r = s[2]
		x = s[3]
		for i in range(left, r):
			l[i] += x


import sys
import numpy as np
from collections import OrderedDict
f = sys.stdin
(n, q) = [int(x) for x in f.readline().split()]
a = [int(x) for x in f.readline().split()]
L = [0] * (n + 1)
R = [0] * (n + 1)
for _ in range(0, q):
	op = [int(x) for x in f.readline().split()]
	if op[0] == 1:
		p = op[1] - 1
		nj = 0
		vis = L[p] - R[p]
		vp = a[p] + vis
		for i in range(p + 1, n):
			dist = i - p
			if dist > 100:
				break
			else:
				vis += L[i] - R[i]
				vi = a[i] + vis
				if vp < vi:
					p = i
					vp = vi
					nj += 1
					if nj >= op[2]:
						break
		print(p + 1)
	else:
		l = op[1] - 1
		r = op[2] - 1
		L[l] += op[3]
		R[r + 1] += op[3]


def query(i, j):
	cnt = 0
	past = arr[i]
	limit = 0
	ind = i
	for idx in range(i + 1, n):
		curr = arr[idx]
		if curr != past and curr > past:
			cnt += 1
			past = curr
			ind = idx
			limit = 0
		if cnt == j:
			return ind + 1
		if curr <= past:
			limit += 1
		if limit > 100:
			break
	return ind + 1

def update(l, r, v):
	for idx in range(l, r + 1):
		arr[idx] += v
(n, q) = list(map(int, input().split()))
arr = list(map(int, input().split()))
for _ in range(q):
	a = list(map(int, input().split()))
	if a[0] - 1:
		update(a[1] - 1, a[2] - 1, a[3])
	else:
		print(query(a[1] - 1, a[2]))


(N, Q) = list(map(int, input().split(' ')))
ar = list(map(int, input().split(' ')))

def find_next(i, k):
	count = 0
	last = i
	ind = i + 1
	while ind < N and count < k:
		if ar[ind] > ar[last] and ind - last <= 100:
			count += 1
			last = ind
		elif ind - last > 100:
			return last
		ind += 1
	if count < k:
		return last
	return ind - 1

def change_height(L, R, K):
	for i in range(L, R + 1):
		ar[i] += K
for _ in range(Q):
	inp = list(map(int, input().split(' ')))
	if inp[0] == 1:
		(i, k) = (inp[1], inp[2])
		print(find_next(i - 1, k) + 1)
	elif inp[0] == 2:
		(L, R, K) = (inp[1], inp[2], inp[3])
		change_height(L - 1, R - 1, K)


(N, Q) = input().split()
N = int(N)
Q = int(Q)
L = list(input().split())
L = list(map(int, L))
while Q > 0:
	L2 = list(input().split())
	L2 = list(map(int, L2))
	le = len(L2)
	i = L2[1] - 1
	k = L2[2]
	if le == 3:
		flag = True
		while flag == True:
			jump = next((z for (z, n) in enumerate(L[i:]) if n > L[i]), len(L) + 1)
			if jump > 100 or jump == len(L) + 1:
				print(i + 1)
				flag = False
			elif k > 0:
				i = i + jump
				k = k - 1
			else:
				print(i + 1)
				flag = False
	else:
		c = L2[3]
		for i in range(i, k):
			L[i] = L[i] + c
	Q = Q - 1


debug = True
(n, q) = list(map(int, input().split()))
a = [0] + list(map(int, input().split()))

def small_inputs():
	p = list(map(int, input().split()))
	if p[0] == 1:
		(i, k) = p[1:]
		c = i
		for j in range(k):
			d = 1
			m = c + 1
			while m <= n and d <= 100:
				if a[m] > a[c]:
					c = m
					break
				d += 1
				m += 1
			if m == n + 1 or d > 100:
				break
		print(c)
	else:
		(l, r, x) = p[1:]
		for i in range(l, r + 1):
			a[i] += x

def large_inputs():
	p = list(map(int, input().split()))
	if p[0] == 1:
		(i, k) = p[1:]
		print(-1)
	else:
		(l, r, x) = p[1:]
for test in range(q):
	if n <= 1000 and q <= 1000:
		small_inputs()
	else:
		large_inputs()


import sys
import numpy
from collections import OrderedDict
f = sys.stdin

def makeJump(op):
	p = op[1] - 1
	nj = 0
	for i in range(p + 1, n):
		dist = i - p
		if dist > 100:
			break
		else:
			vp = a[p]
			vi = a[i]
			for k in [x for x in list(jumps.keys()) if p <= x]:
				d = jumps[k]
				for k2 in d:
					if p >= k2:
						vp += d[k2]
			for k in [x for x in list(jumps.keys()) if i <= x]:
				d = jumps[k]
				for k2 in d:
					if i >= k2:
						vi += d[k2]
			if vp < vi:
				p = i
				nj += 1
		if nj >= op[2]:
			break
	print(p + 1)
	return
(n, q) = [int(x) for x in f.readline().split()]
a = [int(x) for x in f.readline().split()]
queries = []
jumps = {}
for _ in range(0, q):
	op = [int(x) for x in f.readline().split()]
	if op[0] == 1:
		makeJump(op)
	else:
		l = op[1] - 1
		r = op[2] - 1
		x = op[3]
		if not r in jumps:
			jumps[r] = {}
		if not l in jumps[r]:
			jumps[r][l] = 0
		jumps[r][l] += x


(n, q) = list(map(int, input().split()))
arr = list(map(int, input().split()))
for _ in range(q):
	ar = list(map(int, input().split()))
	a = ar[0]
	if a == 1:
		(b, c) = (ar[1], ar[2])
		curr = b - 1
		f = 1
		for i in range(c):
			for j in range(curr, n):
				if arr[j] > arr[curr] and j - curr <= 100:
					curr = j
					break
		print(curr + 1)
	else:
		(b, c, d) = (ar[1], ar[2], ar[3])
		for k in range(b - 1, c):
			arr[k] += d


import sys
import numpy
f = sys.stdin
(n, q) = [int(x) for x in f.readline().split()]
a = [int(x) for x in f.readline().split()]
t2 = []
for _ in range(0, q):
	op = [int(x) for x in f.readline().split()]
	if op[0] == 1:
		p = op[1] - 1
		jumps = 0
		for i in range(p + 1, n):
			dist = i - p
			if dist > 100:
				break
			else:
				vp = a[p]
				vi = a[i]
				for arr2 in t2:
					l = arr2[1] - 1
					r = arr2[2] - 1
					if p >= l and p <= r:
						vp += arr2[3]
					if i >= l and i <= r:
						vi += arr2[3]
				if vp < vi:
					p = i
					jumps += 1
			if jumps >= op[2]:
				break
		print(p + 1)
	else:
		t2.append(op)


from sys import stdin, stdout
(n, q) = list(map(int, stdin.readline().split()))
hillheight = list(map(int, stdin.readline().split()))
for i in range(q):
	t = list(map(int, stdin.readline().split()))
	if t[0] == 1:
		position = t[1] - 1
		numberofjumps = t[2]
		for k in range(position, n):
			if k - position > 100 or numberofjumps == 0:
				break
			if hillheight[k] > hillheight[position]:
				position = k
				numberofjumps = numberofjumps - 1
		stdout.write('{}\n'.format(position + 1))
	elif t[0] == 2:
		L = t[1]
		R = t[2]
		X = t[3]
		for w in range(L - 1, R):
			hillheight[w] = hillheight[w] + X


import sys
ar = list(map(int, input().strip().split(' ')))
n = ar[0]
q = ar[1]
gre = []
for i1 in range(n + 2):
	gre.append(0)
n1 = list(map(int, input().strip().split(' ')))
n1.insert(0, 0)
for i1 in range(q):
	a = list(map(int, input().strip().split(' ')))
	if a[0] == 2:
		l = a[1]
		r = a[2]
		x = a[3]
		gre[l] += x
		gre[r + 1] -= x
	elif a[0] == 1:
		i = a[1]
		k = a[2]
		g = gre[i]
		w1 = i
		m1 = n1[i] + g
		for qw in range(i + 1, n + 1):
			g += gre[qw]
			if qw - w1 > 100:
				break
			if k == 0:
				break
			if n1[qw] + g > m1:
				m1 = n1[qw] + g
				w1 = qw
				k = k - 1
		print(w1)


(n, queries) = list(map(int, input().strip().split()))
arr = list(map(int, input().strip().split()))
for i in range(queries):
	inp = list(map(int, input().strip().split()))
	if inp[0] == 1:
		(curr, maxJumps, out) = (inp[1] - 1, inp[2], inp[1] - 1)
		while maxJumps > 0:
			(i, nextTo) = (curr + 1, curr)
			while i < n and i < curr + 101:
				if arr[i] > arr[curr]:
					nextTo = i
					break
				i += 1
			if nextTo == curr:
				out = nextTo
				break
			out = nextTo
			curr = nextTo
			maxJumps -= 1
		print(out + 1)
	else:
		for i in range(inp[1] - 1, inp[2]):
			arr[i] += inp[3]


inpt = list(map(int, input().split()))
n = inpt[0]
q = inpt[1]
h = list(map(int, input().split()))
for i in range(0, q):
	flag = 1
	oper = list(map(int, input().split()))
	typ = oper[0]
	if typ == 2:
		for j in range(oper[1] - 1, oper[2]):
			h[j] = h[j] + oper[3]
	elif typ == 1:
		start = oper[1] - 1
		pos = start
		jump = oper[2]
		count = 0
		jp = 0
		for l in range(pos + 1, n):
			count = count + 1
			if jp == jump:
				break
			if count > 100:
				break
			if h[l] > h[pos]:
				start = l
				pos = start
				jp = jp + 1
				count = 0
		print(start + 1)