/*  This is an example of Cauchy sequence.        */
/*  About the model, I refered to the wikipedia.  */
/*  Let's enjoy C programming.                    */

# include <stdio.h>
# include <string.h>
# include <math.h>

long double n, x;
void loop_x()
{
	do{
		printf("Please enter X ,which is a natural number, and X<10^8.\n");
		scanf("%Lf", &x);
		if (x<=0){
			printf("As X is positive, %Lf is invalid.\n",x);
		}
		if (x!=(long int)(x)){
			printf("As X is an integer, %Lf is invalid.\n",x);
		}
		if (x>=pow(10.0,8)){
			printf("As X<10^8, %Lf is invalid.\n",x);
		}
	}while(x<0 || x!=(long int)x || x>=pow(10.0,8));
}

void loop_n()
{
	do{
		printf("Please enter N, which is a rational number.0< N<10^16.\n");
		scanf("%Lf", &n);
		if (n<=pow(0.1,16)){
			printf("As 0.1^16<N, %Lf is invalid.\n",n);
		}
		if (n>=pow(10.0,16)){
			printf("As N<10^16, %Lf is invalid.\n",n);
		}
	}while(n<=0 || n>=pow(10.0,16));
}

int main()
{
	int            l;
	long long int  z;
	double         o;
	long double    a, b, c, m;
	char           a1[4], a2[9], a3[14];

	strcpy(a1,"Num");
	strcpy(a2,"log10(N)");
	strcpy(a3,"[N*sqrt{X}]/N");

	loop_x();
	loop_n();

        z=(long long int)(x);
	printf("\n");
	printf("*****************************************\n");
	printf(" An example of Cauchy sequence\n");
	printf(" X = %lld, N = %LE\n",z,n);
	printf("*****************************************\n\n");
	printf("%5s  %21s%21s\n",a1, a2, a3);

	for(l=1;l<=10;l++){
		m=n/pow(10.0,(10.0-l));
		o=log10(m);
		a=m*sqrt(x);
		b=(long long int)(a);
		c = b / m;
		printf("%5d  %21.15lE%21.15Lf\n",l, o, c);
	}
	printf("\n");
	return(0);
}