Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)

Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
if n == 1:
    for i in range(q):
        v, w = [int(item) for item in input().split()]
        print(min(v, w))
    exit()

for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    ans += str(v+1) + "\n"
print(ans)

Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
if n == 1:
    for i in range(q):
        v, w = [int(item) for item in input().split()]
        print(min(v, w))
    exit()

for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    ans += str(v+1) + "\n"
print(ans)

Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
if n == 1:
    for i in range(q):
        v, w = [int(item) for item in input().split()]
        print(min(v, w))
    exit()

for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

n, q = [int(item) for item in input().split()]
for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)

Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

ans = ""
n, q = [int(item) for item in input().split()]
if n == 1:
    for i in range(q):
        v, w = [int(item) for item in input().split()]
        print(min(v, w))
    exit()

for i in range(q):
    v, w = [int(item) - 1 for item in input().split()]
    while v != w:
        if v > w:
            v = (v - 1) // n
        else:
            w = (w - 1) // n
    print(v + 1)