Chef and his friend Bharat have decided to play the game “The Chefora Spell”.
In the game, a positive integer NN (in decimal system) is considered a “Chefora” if the number of digits dd is odd and it satisfies the equationN=∑i=0d−1Ni⋅10i,N=∑i=0d−1Ni⋅10i,
where NiNi is the ii-th digit of NN from the left in 00-based indexing.
Let AiAi denote the ii-th largest Chefora number.
They’ll ask each other QQ questions, where each question contains two integers LL and RR. The opponent then has to answer with(∏i=L+1R(AL)Ai)mod109+7.(∏i=L+1R(AL)Ai)mod109+7.
Bharat has answered all the questions right, and now it is Chef’s turn. But since Chef fears that he could get some questions wrong, you have come to his rescue!
Input
- The first line contains an integer QQ – the number of questions Bharat asks.
- Each of the next QQ lines contains two integers LL and RR.
Output
Print QQ integers – the answers to the questions on separate lines.
Constraints
- 1≤N,Q≤1051≤N,Q≤105
- 1≤L<R≤N1≤L<R≤N
Subtasks
Subtask #1 (30 points): 1≤N,Q≤5⋅1031≤N,Q≤5⋅103
Subtask #2 (70 points): Original constraints
Sample Input
2
1 2
9 11
Sample Output
1
541416750
Explanation
- For the first question:(A1)A2=12=1.(A1)A2=12=1.
- For the second question:(A9)A10⋅(A9)A11=9101⋅9111≡541416750(mod109+7).
SOLUTION
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CPP
#include <iostream>
#include<bits/stdc++.h>
using namespace std;
#define l1 long long
#define mod 1000000007
l1 power(l1 bs, l1 pw){
l1 res=1;
while(pw!=0){
if(pw%2==0){
bs=((bs%mod)*(bs%mod))%mod;
pw=floor(pw/2);
}
else{
res=((res%mod)*(bs%mod))%mod;
pw=pw-1;
}
}
return res;
}
l1 chefona(l1 num){
l1 chefnum=num;
l1 retnum=0;
if(num<10){
retnum=chefnum;
}
else if(num>=10){
num=num/10;
while(num!=0){
chefnum=chefnum*10+num%10;
num=num/10;
}
retnum=chefnum;
}
return retnum;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
l1 a[100001]={0};
l1 prearray[100001]={0};
for(l1 i=1;i<=100001;i++){
a[i]=chefona(i);
prearray[i]=prearray[i-1]+a[i];
}
l1 t;
cin>>t;
while(t--){
l1 l,r;
cin>>l>>r;
l1 diff=prearray[r]-prearray[l];
cout<<power(a[l],diff)<<"\n";
}
return 0;
}
Python
def findpower(base,power):
mod = 10**9+7
res = 1
while power!=0:
if power%2==0:
base = ((base%mod)*(base%mod))%mod
power = power//2
else:
res = ((res%mod)*(base%mod))%mod
power = power-1
return res
def findshefola(num):
palin = num
num = num//10
while num>0:
palin = palin*10+num%10
num = num//10
return palin
arr = [0]*(10**5+1)
arrsm = [0]*(10**5+1)
for i in range(1,10**5+1):
arr[i] = findshefola(i)
arrsm[i] = arrsm[i-1] + arr[i]
for _ in range(int(input())):
l,r = map(int,input().split())
power = arrsm[r]-arrsm[l]
print(findpower(arr[l],power))Read More Post Here
