Dynamic Range Minimum Queries

from math import sqrt

buffer = input().split()
n = int(buffer[0])
q = int(buffer[1])

values = list(map(int,input().split()))

m = int(sqrt(n))
roots = []

def update(k,u):
    values[k] = u
    ri = k//m
    roots[ri] = min(roots[ri], u)

for i in range(m):
    roots.append(min(values[i*m:(i+1)*m]))
roots.append(min(values[m**2:]))

for i in range(q):
    query = input().split()
    qtype = int(query[0])
    a = int(query[1])
    b = int(query[2])
    if qtype == 1:
        a -= 1 #zero-based indexing
        update(a,b)
    elif qtype == 2:
        a -= 1 #zero-based indexing
        b -= 1 #zero-based indexing
        print(min(values[a:b+1]))

Test 1

Verdict: RUNTIME ERROR

Traceback (most recent call last):
  File "/box/input/code.py", line 28, in <module>
    update(a,b)
  File "/box/input/code.py", line 15, in update
    roots[ri] = min(roots[ri], u)
IndexError: list index out of range

Test 2

Verdict: TIME LIMIT EXCEEDED