Problem:


Score : 100 points

Problem Statement

You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

The type of i-th query is represented by T_i.

T_i=1: You are given two integers X_i,V_i. Replace the value of A_{X_i} with V_i.

T_i=2: You are given two integers L_i,R_i. Calculate the maximum value among A_{L_i},A_{L_i+1},\cdots,A_{R_i}.

T_i=3: You are given two integers X_i,V_i. Calculate the minimum j such that X_i \leq j \leq N, V_i \leq A_j. If there is no such j, answer j=N+1 instead.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9

1 \leq Q \leq 2 \times 10^5

1 \leq T_i \leq 3

1 \leq X_i \leq N, 0 \leq V_i \leq 10^9 (T_i=1,3)

1 \leq L_i \leq R_i \leq N (T_i=2)

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 \cdots A_N
First query
Second query
\vdots
Q-th query

Each query is given in the following format:

If T_i=1,3,

T_i X_i V_i

If T_i=2,

T_i L_i R_i

Output

For each query with T_i=2, 3, print the answer.

Sample Input 1

5 5
1 2 3 2 1
2 1 5
3 2 3
1 3 1
2 2 4
3 1 3

Sample Output 1

3
3
2
6

First query: Print 3, which is the maximum of (A_1,A_2,A_3,A_4,A_5)=(1,2,3,2,1).

Second query: Since 3>A_2, j=2 does not satisfy the condition．Since 3 \leq A_3, print j=3.

Third query: Replace the value of A_3 with 1. It becomes A=(1,2,1,2,1).

Fourth query: Print 2, which is the maximum of (A_2,A_3,A_4)=(2,1,2).

Fifth query: Since there is no j that satisfies the condition, print j=N+1=6.



Sample input:
5 5
1 2 3 2 1
2 1 5
3 2 3
1 3 1
2 2 4
3 1 3


Sample output:
3
3
2
6

Submission status: Accepted

Solution code:
class RMaxQ:
    
    __slots__ = ["n", "data", "id"]
    
    def __init__(self, li):
        self.n = len(li)
        self.id = -float("inf")
        self.data = [self.id]*self.n + li
        for i in range(self.n - 1, 0, -1):
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def get(self, i):
        return self.data[i+self.n]
    
    def update(self, i, a):
        i += self.n
        self.data[i] = a
        while i > 1:
            i //= 2
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def add(self, i, a):
        i += self.n
        self.data[i] += a
        while i > 1:
            i //= 2
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def fold(self, l, r):
        l += self.n
        r += self.n
        res = self.id
        while l < r:
            if l % 2:
                res = max(self.data[l], res)
                l += 1
            if r % 2:
                r -= 1
                res = max(res, self.data[r])
            l //= 2
            r //= 2
        return res
    
    def max_right(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (left_li + right_li[::-1]):
            if not check(max(temp, self.data[idx])):
                temp = max(temp, self.data[idx])
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(max(temp, self.data[2*idx])):
                idx = 2*idx
            else:
                temp = max(temp, self.data[2*idx])
                idx = 2*idx+1
        return idx - self.n
    
    def min_left(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (right_li + left_li[::-1]):
            if not check(max(self.data[idx], temp)):
                temp = max(self.data[idx], temp)
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(max(self.data[2*idx+1], temp)):
                idx = 2*idx+1
            else:
                temp = max(temp, self.data[2*idx+1], temp)
                idx = 2*idx
        return idx - self.n

import sys
input = sys.stdin.readline
n, q = map(int, input().split())
A = list(map(int, input().split()))
seg = RMaxQ(A)
for _ in range(q):
    t, x, v = map(int, input().split())
    x -= 1
    if t == 1:
        seg.update(x, v)
    elif t == 2:
        print(seg.fold(x, v))
    else:
        ans = seg.max_right(x, n, lambda x: x>=v)
        if ans == -1:
            print(n+1)
        else:
            print(ans+1)

Submission status: Accepted

Solution code:
class RMaxQ:
    
    __slots__ = ["n", "data"]
    
    def __init__(self, li):
        self.n = len(li)
        self.data = [-float("inf")]*self.n + li
        for i in range(self.n - 1, 0, -1):
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def get(self, i):
        return self.data[i+self.n]
    
    def update(self, i, a):
        i += self.n
        self.data[i] = a
        while i > 1:
            i //= 2
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def add(self, i, a):
        i += self.n
        self.data[i] += a
        while i > 1:
            i //= 2
            self.data[i] = max(self.data[2*i], self.data[2*i+1])
    
    def fold(self, l, r):
        l += self.n
        r += self.n
        res = -float("inf")
        while l < r:
            if l % 2:
                res = max(self.data[l], res)
                l += 1
            if r % 2:
                r -= 1
                res = max(res, self.data[r])
            l //= 2
            r //= 2
        return res
    
    def max_right(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = -float("inf")
        for idx in (left_li + right_li[::-1]):
            if not check(max(temp, self.data[idx])):
                temp = max(temp, self.data[idx])
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(max(temp, self.data[2*idx])):
                idx = 2*idx
            else:
                temp = max(temp, self.data[2*idx])
                idx = 2*idx+1
        return idx - self.n
    
    def min_left(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = -float("inf")
        for idx in (right_li + left_li[::-1]):
            if not check(max(self.data[idx], temp)):
                temp = max(self.data[idx], temp)
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(max(self.data[2*idx+1], temp)):
                idx = 2*idx+1
            else:
                temp = max(temp, self.data[2*idx+1], temp)
                idx = 2*idx
        return idx - self.n

import sys
input = sys.stdin.readline
n, q = map(int, input().split())
A = list(map(int, input().split()))
seg = RMaxQ(A)
for _ in range(q):
    t, x, v = map(int, input().split())
    x -= 1
    if t == 1:
        seg.update(x, v)
    elif t == 2:
        print(seg.fold(x, v))
    else:
        ans = seg.max_right(x, n, lambda x: x>=v)
        if ans == -1:
            print(n+1)
        else:
            print(ans+1)

Submission status: Accepted

Solution code:
class SegTree:
    
    __slots__ = ["n", "data", "f", "id"]
    
    def __init__(self, li, func, identity):
        self.n = len(li)
        self.f = func
        self.id = identity
        self.data = [self.id]*self.n + li
        for i in range(self.n - 1, 0, -1):
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def get(self, i):
        return self.data[i+self.n]
    
    def update(self, i, a):
        i += self.n
        self.data[i] = a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def add(self, i, a):
        i += self.n
        self.data[i] += a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def fold(self, l, r):
        l += self.n
        r += self.n
        res = self.id
        while l < r:
            if l % 2:
                res = self.f(self.data[l], res)
                l += 1
            if r % 2:
                r -= 1
                res = self.f(res, self.data[r])
            l //= 2
            r //= 2
        return res
    
    def max_right(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (left_li + right_li[::-1]):
            if not check(self.f(temp, self.data[idx])):
                temp = self.f(temp, self.data[idx])
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(temp, self.data[2*idx])):
                idx = 2*idx
            else:
                temp = self.f(temp, self.data[2*idx])
                idx = 2*idx+1
        return idx - self.n
    
    def min_left(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (right_li + left_li[::-1]):
            if not check(self.f(self.data[idx], temp)):
                temp = self.f(self.data[idx], temp)
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(self.data[2*idx+1], temp)):
                idx = 2*idx+1
            else:
                temp = self.f(temp, self.data[2*idx+1], temp)
                idx = 2*idx
        return idx - self.n

import sys
input = sys.stdin.readline
n, q = map(int, input().split())
A = list(map(int, input().split()))
seg = SegTree(A, max, -float("inf"))
for _ in range(q):
    t, x, v = map(int, input().split())
    x -= 1
    if t == 1:
        seg.update(x, v)
    elif t == 2:
        print(seg.fold(x, v))
    else:
        ans = seg.max_right(x, n, lambda x: x>=v)
        if ans == -1:
            print(n+1)
        else:
            print(ans+1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline


class SegTree:
    def __init__(self, v, op, e) -> None:
        self._n = len(v)
        self.log = (self._n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e for _ in range(2 * self.size)]
        self.op = op
        self.e = e
        for i in range(self._n):
            self.d[self.size + i] = v[i]
        for i in reversed(range(1, self.size)):
            self.__update__(i)

    @classmethod
    def init_e(cls, n: int, op, e) -> 'SegTree':
        return cls([e for _ in range(n)], op, e)

    def set(self, p: int, x) -> None:
        p += self.size
        self.d[p] = x
        for i in range(1, self.log + 1):
            self.__update__(p >> i)

    def get(self, p: int):
        return self.d[p + self.size]

    def prod(self, l: int, r: int):
        sml = self.e
        smr = self.e
        l += self.size
        r += self.size

        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self):
        return self.d[1]

    def max_right(self, l: int, f):
        if l == self._n:
            return self._n
        l += self.size
        sm = self.e
        while True:
            while l & 1 == 0:
                l >>= 1
            if not f(self.op(sm, self.d[l])):
                while l < self.size:
                    l <<= 1
                    if f(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l:
                return self._n

    def min_left(self, r: int, f):
        if r == 0:
            return 0
        r += self.size
        sm = self.e
        while True:
            r -= 1
            while r > 1 and r & 1:
                r >>= 1
            if not f(self.op(self.d[r], sm)):
                while r < self.size:
                    r = (r << 1) + 1
                    if f(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r:
                return 0

    def __update__(self, k: int) -> None:
        self.d[k] = self.op(self.d[k << 1], self.d[(k << 1) + 1])


n, q = map(int, input().split())
a = list(map(int, input().split()))
seg = SegTree(a, max, -1)

for _ in range(q):
    t, x, y = map(int, input().split())
    if t == 1:
        seg.set(x - 1, y)
    elif t == 2:
        print(seg.prod(x - 1, y))
    else:
        print(seg.max_right(x - 1, lambda v: v < y) + 1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline


class SegTree:
    def __init__(self, v, op, e) -> None:
        self._n = len(v)
        self.log = (self._n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e() for _ in range(2 * self.size)]
        self.op = op
        self.e = e
        for i in range(self._n):
            self.d[self.size + i] = v[i]
        for i in reversed(range(1, self.size)):
            self.__update__(i)

    @classmethod
    def init_e(cls, n: int, op, e) -> 'SegTree':
        return cls([e for _ in range(n)], op, e)

    def set(self, p: int, x) -> None:
        p += self.size
        self.d[p] = x
        for i in range(1, self.log + 1):
            self.__update__(p >> i)

    def get(self, p: int):
        return self.d[p + self.size]

    def prod(self, l: int, r: int):
        sml = self.e()
        smr = self.e()
        l += self.size
        r += self.size

        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self):
        return self.d[1]

    def max_right(self, l: int, f):
        if l == self._n:
            return self._n
        l += self.size
        sm = self.e()
        while True:
            while l & 1 == 0:
                l >>= 1
            if not f(self.op(sm, self.d[l])):
                while l < self.size:
                    l <<= 1
                    if f(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l:
                return self._n

    def min_left(self, r: int, f):
        if r == 0:
            return 0
        r += self.size
        sm = self.e()
        while True:
            r -= 1
            while r > 1 and r & 1:
                r >>= 1
            if not f(self.op(self.d[r], sm)):
                while r < self.size:
                    r = (r << 1) + 1
                    if f(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r:
                return 0

    def __update__(self, k: int) -> None:
        self.d[k] = self.op(self.d[k << 1], self.d[(k << 1) + 1])


n, q = map(int, input().split())
a = list(map(int, input().split()))
seg = SegTree(a, max, lambda: -1)

for _ in range(q):
    t, x, y = map(int, input().split())
    if t == 1:
        seg.set(x - 1, y)
    elif t == 2:
        print(seg.prod(x - 1, y))
    else:
        print(seg.max_right(x - 1, lambda v: v < y) + 1)

Submission status: Accepted

Solution code:
class SegTree:
    
    __slots__ = ["n", "data", "f", "id"]
    
    def __init__(self, li, func, identity):
        self.n = len(li)
        self.f = func
        self.id = identity
        self.data = [None]*self.n + li
        for i in range(self.n - 1, 0, -1):
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def get(self, i):
        return self.data[i+self.n]
    
    def update(self, i, a):
        i += self.n
        self.data[i] = a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def add(self, i, a):
        i += self.n
        self.data[i] += a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def fold(self, l, r):
        l += self.n
        r += self.n
        res = self.id
        while l < r:
            if l % 2:
                res = self.f(self.data[l], res)
                l += 1
            if r % 2:
                r -= 1
                res = self.f(res, self.data[r])
            l //= 2
            r //= 2
        return res
    
    def max_right(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (left_li + right_li[::-1]):
            if not check(self.f(temp, self.data[idx])):
                temp = self.f(temp, self.data[idx])
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(temp, self.data[2*idx])):
                idx = 2*idx
            else:
                temp = self.f(temp, self.data[2*idx])
                idx = 2*idx+1
        return idx - self.n
    
    def min_left(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (right_li + left_li[::-1]):
            if not check(self.f(self.data[idx], temp)):
                temp = self.f(self.data[idx], temp)
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(self.data[2*idx+1], temp)):
                idx = 2*idx+1
            else:
                temp = self.f(temp, self.data[2*idx+1], temp)
                idx = 2*idx
        return idx - self.n

import sys
input = sys.stdin.readline
n, q = map(int, input().split())
A = list(map(int, input().split()))
seg = SegTree(A, max, -1)
for _ in range(q):
    t, x, v = map(int, input().split())
    x -= 1
    if t == 1:
        seg.update(x, v)
    elif t == 2:
        print(seg.fold(x, v))
    else:
        ans = seg.max_right(x, n, lambda x: x>=v)
        if ans == -1:
            print(n+1)
        else:
            print(ans+1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline


class SegTree:
    def __init__(self, v, op, e) -> None:
        self._n = len(v)
        self.log = (self._n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e() for _ in range(2 * self.size)]
        self.op = op
        self.e = e
        for i in range(self._n):
            self.d[self.size + i] = v[i]
        for i in reversed(range(1, self.size)):
            self.__update__(i)

    @classmethod
    def init_e(cls, n: int, op, e) -> 'SegTree':
        return cls([e for _ in range(n)], op, e)

    def set(self, p: int, x) -> None:
        p += self.size
        self.d[p] = x
        for i in range(1, self.log + 1):
            self.__update__(p >> i)

    def get(self, p: int):
        return self.d[p + self.size]

    def prod(self, l: int, r: int):
        sml = self.e()
        smr = self.e()
        l += self.size
        r += self.size

        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self):
        return self.d[1]

    def max_right(self, l: int, f):
        if l == self._n:
            return self._n
        l += self.size
        sm = self.e()
        while True:
            while l % 2 == 0:
                l >>= 1
            if not f(self.op(sm, self.d[l])):
                while l < self.size:
                    l *= 2
                    if f(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l:
                return self._n

    def min_left(self, r: int, f):
        if r == 0:
            return 0
        r += self.size
        sm = self.e()
        while True:
            r -= 1
            while r > 1 and r % 2:
                r >>= 1
            if not f(self.op(self.d[r], sm)):
                while r < self.size:
                    r = 2 * r + 1
                    if f(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r:
                return 0

    def __update__(self, k: int) -> None:
        self.d[k] = self.op(self.d[2 * k], self.d[2 * k + 1])


n, q = map(int, input().split())
a = list(map(int, input().split()))
seg = SegTree(a, max, lambda: -1)

for _ in range(q):
    t, x, y = map(int, input().split())
    if t == 1:
        seg.set(x - 1, y)
    elif t == 2:
        print(seg.prod(x - 1, y))
    else:
        print(seg.max_right(x - 1, lambda v: v < y) + 1)

Submission status: Accepted

Solution code:
class SegTree:
    
    __slots__ = ["n", "data", "f", "id"]
    
    def __init__(self, li, func, identity):
        self.n = len(li)
        self.f = func
        self.id = identity
        self.data = [self.id]*self.n + li
        for i in range(self.n - 1, 0, -1):
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def get(self, i):
        return self.data[i+self.n]
    
    def update(self, i, a):
        i += self.n
        self.data[i] = a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def add(self, i, a):
        i += self.n
        self.data[i] += a
        while i > 1:
            i //= 2
            self.data[i] = self.f(self.data[2*i], self.data[2*i+1])
    
    def fold(self, l, r):
        l += self.n
        r += self.n
        res = self.id
        while l < r:
            if l % 2:
                res = self.f(self.data[l], res)
                l += 1
            if r % 2:
                r -= 1
                res = self.f(res, self.data[r])
            l //= 2
            r //= 2
        return res
    
    def max_right(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (left_li + right_li[::-1]):
            if not check(self.f(temp, self.data[idx])):
                temp = self.f(temp, self.data[idx])
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(temp, self.data[2*idx])):
                idx = 2*idx
            else:
                temp = self.f(temp, self.data[2*idx])
                idx = 2*idx+1
        return idx - self.n
    
    def min_left(self, l, r, check):
        l += self.n
        r += self.n
        left_li = []
        right_li = []
        while l < r:
            if l % 2:
                left_li.append(l)
                l += 1
            if r % 2:
                r -= 1
                right_li.append(r)
            l //= 2
            r //= 2
        temp = self.id
        for idx in (right_li + left_li[::-1]):
            if not check(self.f(self.data[idx], temp)):
                temp = self.f(self.data[idx], temp)
            else:
                break
        else:
            return -1
        while idx < self.n:
            if check(self.f(self.data[2*idx+1], temp)):
                idx = 2*idx+1
            else:
                temp = self.f(temp, self.data[2*idx+1], temp)
                idx = 2*idx
        return idx - self.n

import sys
input = sys.stdin.readline
n, q = map(int, input().split())
A = list(map(int, input().split()))
seg = SegTree(A, max, -1)
for _ in range(q):
    t, x, v = map(int, input().split())
    x -= 1
    if t == 1:
        seg.update(x, v)
    elif t == 2:
        print(seg.fold(x, v))
    else:
        ans = seg.max_right(x, n, lambda x: x>=v)
        if ans == -1:
            print(n+1)
        else:
            print(ans+1)

Submission status: Accepted

Solution code:
from typing import Callable, TypeVar, List
import sys
input = sys.stdin.readline
T = TypeVar('T')


class SegTree:
    def __init__(self, v: List[T], op: Callable[[T, T], T], e: Callable[[], T]) -> None:
        self._n = len(v)
        self.log = (self._n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e() for _ in range(2 * self.size)]
        self.op = op
        self.e = e
        for i in range(self._n):
            self.d[self.size + i] = v[i]
        for i in reversed(range(1, self.size)):
            self.d[i] = self.op(self.d[2 * i], self.d[2 * i + 1])

    @classmethod
    def init_e(cls, n: int, op: Callable[[T, T], T], e: Callable[[], T]) -> 'SegTree':
        return cls([e for _ in range(n)], op, e)

    def set(self, p: int, x: T) -> None:
        assert 0 <= p < self._n
        p += self.size
        self.d[p] = x
        for i in range(1, self.log + 1):
            k = p >> i
            self.d[k] = self.op(self.d[2 * k], self.d[2 * k + 1])

    def get(self, p: int) -> T:
        assert 0 <= p < self._n
        return self.d[p + self.size]

    def prod(self, l: int, r: int) -> T:
        assert 0 <= l <= self._n and 0 <= r <= self._n
        sml = self.e()
        smr = self.e()
        l += self.size
        r += self.size

        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self) -> T:
        return self.d[1]

    def max_right(self, l: int, f: Callable[[T], bool]):
        assert 0 <= l <= self._n
        assert f(self.e())
        if l == self._n:
            return self._n
        l += self.size
        sm = self.e()
        while True:
            while l % 2 == 0:
                l >>= 1
            if not f(self.op(sm, self.d[l])):
                while l < self.size:
                    l *= 2
                    if f(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l:
                return self._n

    def min_left(self, r: int, f: Callable[[T], bool]):
        assert 0 <= r <= self._n
        assert f(self.e())
        if r == 0:
            return 0
        r += self.size
        sm = self.e()
        while True:
            r -= 1
            while r > 1 and r % 2:
                r >>= 1
            if not f(self.op(self.d[r], sm)):
                while r < self.size:
                    r = 2 * r + 1
                    if f(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r:
                return 0

    def __update__(self, k: int) -> None:
        self.d[k] = self.op(self.d[2 * k], self.d[2 * k + 1])


n, q = map(int, input().split())
a = list(map(int, input().split()))
seg = SegTree(a, max, lambda: -1)

for _ in range(q):
    t, x, y = map(int, input().split())
    if t == 1:
        seg.set(x - 1, y)
    elif t == 2:
        print(seg.prod(x - 1, y))
    else:
        print(seg.max_right(x - 1, lambda v: v < y) + 1)