圆相切半径4园

Three circles $CaC_{a}Ca, CbC_{b}Cb, and CcC_{c}Cc, all with radius RRR and tangent to each other, are located in two-dimensional space as shown in Figure 111. A smaller circle C1C_{1}C1 with radius R1R_{1}R1 (R1<RR_{1}<RR1<R) is then inserted into the blank area bounded by CaC_{a}Ca, CbC_{b}Cb, and CcC_{c}Cc so that C1C_{1}C1 is tangent to the three outer circles, CaC_{a}Ca, CbC_{b}Cb, and CcC_{c}Cc. Now, we keep inserting a number of smaller and smaller circles Ck (2≤k≤N)C_{k} (2 leq k leq N)Ck (2≤k≤N) with the corresponding radius RkR_{k}Rk into the blank area bounded by CaC_{a}Ca, CcC_{c}Cc and Ck−1C_{k-1}Ck−1 (2≤k≤N)(2 leq k leq N)(2≤k≤N), so that every time when the insertion occurs, the inserted circle CkC_{k}Ck is always tangent to the three outer circles CaC_{a}Ca, CcC_{c}Cc and Ck−1C_{k-1}Ck−1, as shown in Figure 111$

Figure 1.

(Left) Inserting a smaller circle $C1C_{1}C1 into a blank area bounded by the circle CaC_{a}Ca, CbC_{b}Cb and CcC_{c}Cc.$

(Right) An enlarged view of inserting a smaller and smaller circle $CkC_{k}Ck into a blank area bounded by CaC_{a}Ca, CcC_{c}Cc and Ck−1C_{k-1}Ck−1 (2≤k≤N2 leq k leq N2≤k≤N), so that the inserted circle CkC_{k}Ck is always tangent to the three outer circles, CaC_{a}Ca, CcC_{c}Cc, and Ck−1C_{k-1}Ck−1.$

Now, given the parameters $RkR_{k}Rk, i.e., the radius of the k−thk-thk−th inserted circle. Please note that since the value of RkR_kRk may not be an integer, you only need to report the integer part of RkR_{k}Rk. For example, if you find that RkR_{k}Rk = 1259.89981259.89981259.8998 for some kkk, then the answer you should report is 125912591259.$

Another example, if $RkR_{k}Rk = 39.102939.102939.1029 for some kkk, then the answer you should report is 393939.$

Assume that the total number of the inserted circles is no more than

$104≤R≤10710^{4} leq R leq 10^{7}104≤R≤107.$

Input Format

Contains

Line

Output Format

Contains

Line $RkR_{k}Rk ----------------output for the value of kkk and RkR_{k}Rk at the test case #111, each of which should be separated by a blank.$

Line $RkR_{k}Rk ----------------output for kkk and the value of RkR_{k}Rk at the test case # iii, each of which should be separated by a blank.$

Line $RkR_{k}Rk ----------------output for kkk and the value ofRkR_{k}Rk at the test case # lll, each of which should be separated by a blank.$

样例输入

样例输出

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#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
int main(){
    int T,n;
    double R;
    while(scanf("%d",&T),T!=-1){
        scanf("%lf",&R);
        while(T--){
            scanf("%d",&n);
            double k1=1/R,k2=1/R,k3=1/R;
            double ans;
            for(int i=0;i<n;++i) {
                double B=-2*(k1+k2+k3);
                double C=-(k1+k2+k3)*(k1+k2+k3)+2*(k1*k1+k2*k2+k3*k3);
                double D=B*B-4*C;
                double k4=(-B+sqrt(D))/2;
                ans=1/k4;
                k3=k4;
            }
            printf("%d %d
",n,floor(ans));
        }
    }
}