public class Solution {

// start from the highest digit of num1, multiply each digit of num2

public String multiply(String num1, String num2) {

// Start typing your Java solution below

// DO NOT write main() function

int[] res = new int[num1.length() + num2.length()];

for (int i = num2.length() - 1; i >= 0; --i) {

int carry = 0;

for (int j = num1.length() - 1; j >=0; --j) {

int tmp = carry + res[i + j + 1] + (num1.charAt(j) - '0') * (num2.charAt(i) - '0');

res[i + j + 1] = tmp % 10;

carry = tmp / 10;

}

res[i] = carry; // put carry to higher digit

}

int i = 0;

StringBuilder sb = new StringBuilder();

while (i < res.length - 1 && res[i] == 0) { // remove leading 0s

++i;

}

while (i < res.length) {

sb.append(res[i++]);

}

return sb.toString();

}

}