public static int[] multiplynew(int[] arr1, int[] arr2){
        int len1 = arr1.length;
        int len2 = arr2.length;
        int len = len1 + len2;
        int[][] arr = new int[len1][len1+len2];

        for(int i=len2-1; i >= 0; i--){
            int carry = 0;
            int j=0;
            for(j=len1-1; j >= 0; j--){
                int shiftLeft = i + 1;
                arr[i][j + shiftLeft] = (arr1[j]*arr2[i] + carry) %10;
                carry = (arr1[j]*arr2[i]+carry) / 10;
            }
            arr[i][(i+1)+j] = carry;
        }

        int[] total = new int[len];
        int carry = 0;
        for(int j=len-1; j >= 0; j--){
            int s=0;
            for(int i=0; i < len2; i++){
                s += arr[i][j];
            }
            total[j] = (s + carry) % 10;
            carry = (s + carry)/10;
        }
        return total;
    }
    

	  // {1, 2, 3} x 3
	  public static int[] multiArr(int[] arr, int n){
		int len = arr.length;
		int c = 0;
		int[] ret = new int[len + 1];
		int lret = len + 1;
		for(int i = 0; i < len; i++){
			int s = arr[len - 1 - i] * n + c;
			ret[lret - 1 - i] = s % 10;
			c = s / 10;
		}
		ret[0] = c;
		return ret;
	}
	

	  public static int[] sumColumn(int[][] arr){
		int[] ret = new int[arr[0].length];
		int c = 0;
		for(int i = 0; i < arr[0].length; i++){
			int rIx = arr[0].length - 1 - i;
			
			int s = 0;
			for(int j = 0; j < arr.length; j++){
				s += arr[j][rIx];
			}
			ret[rIx] = (s + c) % 10;
			c = (s + c) / 10;
		}
		ret[0] = c;
		return ret;
	}

	

     /**
                1 2 3
                  2 3


       
                 1 2 3          <- a
                       3
                       2
                       ↑
                       b

     */
    public static int[] multiLongInteger(int[] a, int[] b){
        int len1 = a.length;
        int len2 = b.length;
        int[][] arr = new int[len2][len1 + len2];
        int lena = len1 + len2;
        for(int i = 0; i < len2; i++){
            int[] c = multiArr(a, b[b.length - 1 - i]);
            for(int j = 0; j < c.length; j++){
                arr[i][lena - 1 - j - i] = c[c.length - 1 - j];
            }
        }
        printArr2d(arr);
        
        return sumColumn(arr);
    }