// program to multiply two polynomials


#include<stdio.h>
void multiply(double f[], double g[], double h[], int m, int n, int *k);

int main()
{

	double f[10],g[10],h[20];
	int m,n,k,i,j;

	printf("enter the degrees of two polynomials f and g values should be <=9 \n");
	scanf("%d %d",&m,&n);
	
	// enter the coefficients of polynomial f and store such that f[0] contains x^0 coefficient f[1] contains x^1 coefficient and so on....
	printf("enter the coefficients of polynomial f\n");
	for(i=0;i<=m;i++)
	scanf("%lf",&f[i]);
	
	// enter the coefficients of polynomial g and store such that g[0] contains x^0 coefficient g[1] contains x^1 coefficient and so on....
	printf("enter the coefficients of polynomial g\n");
	for(i=0;i<=n;i++)
	scanf("%lf",&g[i]);

	multiply(f,g,h,m,n,&k);

	printf("result of multiplying polynoimials\n");
	for(i=m;i>0;i--)
	printf("%lf * x^%d + ",f[i],i);
	printf("%lf * x^%d  ",f[i],i);
	
	printf("\n and\n");

	for(i=n;i>0;i--)
	printf("%lf * x^%d + ",g[i],i);
	printf("%lf * x^%d  ",g[i],i);
	printf("\n is\n");
	
	for(i=k;i>0;i--)
	printf("%lf * x^%d + ",h[i],i);
	printf("%lf * x^%d  ",g[i],i);
	

	//for(i=0;i<=k;i++)
	//printf("%lf \t",h[i]);
	return 0;
}

// function to multiply

void multiply(double f[], double g[], double h[], int m, int n, int *k)
{

	int i,j;	
	//order of resulting polynomial 
	*k=m+n;

	for(i=0;i<=*k;i++)
	h[i]=0.0;

	for(i=0;i<=n;i++)
	{
		for(j=0;j<=m;j++)
		{
			h[i+j]+=f[j]*g[i];
		}
	}
}