ACM 第十一天

多校7题目

GuGuFishtion

Time Limit: 3000/1500 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1008    Accepted Submission(s): 175

Problem Description

Today XianYu is too busy with his homework, but the boring GuGu is still disturbing him!!!!!!
At the break time, an evil idea arises in XianYu's mind.
‘Come on, you xxxxxxx little guy.’
‘I will give you a function ϕ(x) which counts the positive integers up to x that are relatively prime to x.’
‘And
now I give you a fishtion, which named GuGu Fishtion, in memory of a
great guy named XianYu and a disturbing and pitiful guy GuGu who will be
cooked without solving my problem in 5 hours.’
‘The given fishtion is defined as follow:

Gu(a,b)=ϕ(ab)ϕ(a)ϕ(b)

And now you, the xxxxxxx little guy, have to solve the problem below given m,n,p.’

(∑a=1m∑b=1nGu(a,b))(modp)

So SMART and KINDHEARTED you are, so could you please help GuGu to solve this problem?
‘GU GU!’ GuGu thanks.

 

Input

Input contains an integer T indicating the number of cases, followed by T lines. Each line contains three integers m,n,p as described above.
1≤T≤3
1≤m,n≤1,000,000
max(m,n)<p≤1,000,000,007
And given p is a prime.

 

Output

Please output exactly T lines and each line contains only one integer representing the answer.

 

Sample Input

1
5 7 23

 

Sample Output

2

 

 

 

Sequence

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1782    Accepted Submission(s): 377

Problem Description

Let us define a sequence as below

⎧⎩⎨⎪⎪⎪⎪⎪⎪F1F2Fn===ABC⋅Fn−2+D⋅Fn−1+⌊Pn⌋

Your job is simple, for each task, you should output Fn module 109+7.

 

Input

The first line has only one integer T, indicates the number of tasks.

Then, for the next T lines, each line consists of 6 integers, A , B, C, D, P, n.

1≤T≤200≤A,B,C,D≤1091≤P,n≤109

 

Sample Input

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

 

Sample Output

36
24

 

v judge 练习题

A - Round House

Vasya lives in a round building, whose entrances are numbered sequentially by integers from 1 to n. Entrance n and entrance 1 are adjacent.

Today Vasya got bored and decided to take a walk in the yard. Vasya lives in entrance a and he decided that during his walk he will move around the house b entrances in the direction of increasing numbers (in this order entrance n should be followed by entrance 1). The negative value of b corresponds to moving |b| entrances in the order of decreasing numbers (in this order entrance 1 is followed by entrance n). If b = 0, then Vasya prefers to walk beside his entrance.

Illustration for n = 6, a = 2, b =  - 5.

Help Vasya to determine the number of the entrance, near which he will be at the end of his walk.

Input

The single line of the input contains three space-separated integers n, a and b (1 ≤ n ≤ 100, 1 ≤ a ≤ n,  - 100 ≤ b ≤ 100) — the number of entrances at Vasya's place, the number of his entrance and the length of his walk, respectively.

Output

Print a single integer k (1 ≤ k ≤ n) — the number of the entrance where Vasya will be at the end of his walk.

Examples

Input

6 2 -5

Output

3

Input

5 1 3

Output

4

Input

3 2 7

Output

3

Note

The first example is illustrated by the picture in the statements.

 #include<stdio.h>

 int main()
 {
     int n;
     int a,b;
     int ans;
     scanf("%d%d %d",&n,&a,&b);
     if(b<)
     {
         int s=b%n;
         if(s==) ans=a;
         else{
         ans=a+(n+(b%n));
         if(ans>n)
         ans=ans%n;}
     }
     else if(b==)  ans=a;
     else
     {

         ans=a+(b%n);
         if(ans>n)  ans=ans%n;
     }
     printf("%d\n",ans);
     return ;
 }