Buggy python submission (verdict: Time Limit Exceeded):
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)


Fixed submission:
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    if n==1:
        print(min(u,v))
        continue
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(u-1)//(n*n)
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(v-1)//(n*n)
            else:
                v=(v-1)//n
    print(u+1)


Fixed submission:
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    if n==1:
        print(min(u,v))
        continue
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)

Buggy python submission (verdict: Runtime Error):
import sys
import math
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    u-=1
    v-=1
    while u!=v:
        if u>v:
            u=(u-1)//(n**(max(1,math.floor(math.log(n,u/(1.0*v))-1))))
        else:
            v=(v-1)//(n**(max(1,math.floor(math.log(n,v/(1.0*v))-1))))
    print(u+1)


Fixed submission:
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    if n==1:
        print(min(u,v))
        continue
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    u-=1
    v-=1
    while u!=v:
        if u>v:
            u=(u-1)//n
        else:
            v=(v-1)//n
    print(u+1)


Fixed submission:
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    if n==1:
        print(min(u,v))
        continue
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)

Buggy python submission (verdict: Time Limit Exceeded):
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    u-=1
    v-=1
    while u!=v:
        if u>v:
            u=(u-1)//n
        else:
            v=(v-1)//n
    print(u+1)

Fixed submission:
import sys
input=sys.stdin.readline
n,q=map(int,input().split())
for i in range(q):
    u,v=map(int,input().split())
    if n==1:
        print(min(u,v))
        continue
    u-=1
    v-=1
    while u!=v:
        if u>v:
            if (u-1)//n>v:
                u=(((u-1)//n)-1)//n
            else:
                u=(u-1)//n
        else:
            if (v-1)//n>v:
                v=(((v-1)//n)-1)//n
            else:
                v=(v-1)//n
    print(u+1)