N children are sitting in a circle to play a game.

The children are numbered from 1 to N in clockwise order. Each of them has a card with a non-zero integer on it in his/her hand. The game starts from the K-th child, who tells all the others the integer on his card and jumps out of the circle. The integer on his card tells the next child to jump out. Let A denote the integer. If A is positive, the next child will be the A-th child to the left. If A is negative, the next child will be the (?A)-th child to the right.

The game lasts until all children have jumped out of the circle. During the game, the p-th child jumping out will get F(p) candies where F(p) is the number of positive integers that perfectly divide p. Who gets the most candies?

Output one line for each test case containing the name of the luckiest child and the number of candies he/she gets. If ties occur, always choose the child who jumps out of the circle first.

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#define Max 500005
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
using namespace std;
int tree[Max<<2];
int RPrime[]={//反素数  
    1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,10080,15120,  
    20160,25200,27720,45360,50400,55440,83160,110880,166320,221760,277200,332640,498960,  
    554400  
};  
  
int fact[]={//反素数约数个数  
    1,2,3,4,6,8,9,10,12,16,18,20,24,30,32,36,40,48,60,64,72,80,84,90,96,100,108,120,128,  
    144,160,168,180,192,200,216  
};  
struct 
{
	int num;
	char name[11];
}child[500005];
void build(int l,int r,int rt)
{
	if(l==r)
	{
		tree[rt]=1;
		return ;
	}
	tree[rt]=r-l+1;
	int m=(l+r)>>1;
	build(lson);
	build(rson);
}
int del(int pos,int l,int r,int rt)
{
	int ans;
	tree[rt]--;
	if(l==r)
		return l;
	int m=(l+r)>>1;
	if(pos<=tree[rt<<1])
		ans=del(pos,lson);
	else
		ans=del(pos-tree[rt<<1],rson);
	return ans;
}
int main()
{
	int i,n,k,mod,p,flag,t,pre,tmp;
	bool circle;
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
	while(scanf("%d%d",&n,&k)!=-1)
	{
		tmp=k;
		flag=0;
		mod=n;
		circle=false;
		build(1,n,1);
		for(i=1;i<=n;i++)
			scanf("%s%d",&child[i].name,&child[i].num);
		for(i=0;RPrime[i]<=n;i++)
		{
			flag=RPrime[i];
			t=i;
		}
		child[0].num=0;
		p=pre=0;
		for(i=1;i<=flag;i++)
		{
			if(child[p].num>0)
			    k=((k+child[p].num-2)%mod+mod)%mod+1;
			else
			    k=((k+child[p].num-1)%mod+mod)%mod+1;
			p=del(k,1,n,1);
			if(p==pre)
			{
				circle=true;
				break;
			}
			pre=p;
			mod--;
		}
		if(circle)
			printf("%s %d\n",child[tmp].name,1);
		else
			printf("%s %d\n",child[p].name,fact[t]);
	}
	return 0;
}