Problem:
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Matrix Vector Multiplication

Write a program which reads a $ n \times m$ matrix $A$ and a $m \times 1$ vector $b$, and prints their product $Ab$.

A column vector with m elements is represented by the following equation.

\[
b = \left(
\begin{array}{c}
b_1 \\
b_2 \\
: \\
b_m \\
\end{array}
\right)
\]

A $n \times m$ matrix with $m$ column vectors, each of which consists of $n$ elements, is represented by the following equation.

\[
A = \left(
\begin{array}{cccc}
a_{11} & a_{12} & ... & a_{1m} \\
a_{21} & a_{22} & ... & a_{2m} \\
: & : & : & : \\
a_{n1} & a_{n2} & ... & a_{nm} \\
\end{array}
\right)
\]

$i$-th element of a $m \times 1$ column vector $b$ is represented by $b_i$ ($i = 1, 2, ..., m$), and the element in $i$-th row and $j$-th column of a matrix $A$ is represented by $a_{ij}$ ($i = 1, 2, ..., n,$ $j = 1, 2, ..., m$).

The product of a $n \times m$ matrix $A$ and a $m \times 1$ column vector $b$ is a $n \times 1$ column vector $c$, and $c_i$ is obtained by the following formula:

\[
c_i = \sum_{j=1}^m a_{ij}b_j = a_{i1}b_1 + a_{i2}b_2 + ... + a_{im}b_m
\]

Input

In the first line, two integers $n$ and $m$ are given. In the following $n$ lines, $a_{ij}$ are given separated by a single space character. In the next $m$ lines, $b_i$ is given in a line.

Output

The output consists of $n$ lines. Print $c_i$ in a line.

Constraints

$1 \leq n, m \leq 100$

$0 \leq b_i, a_{ij} \leq 1000$

Sample Input

3 4
1 2 0 1
0 3 0 1
4 1 1 0
1
2
3
0

Sample Output

5
6
9

Solution in JAVA (judge verdict: Runtime Error)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
    public static void main(String[] args) {
        try {
            BufferedReader stdReader = new BufferedReader(new InputStreamReader(System.in));
            
            String line;
            int count = 0;
            int nc = 0;
            int mc = 0;
            int n = 1;
            int m = 1;
            ArrayList<Integer> matrix = new ArrayList<Integer>();
            ArrayList<Integer> vector = new ArrayList<Integer>();
            
            while((line = stdReader.readLine()) != null) {
                // ????????????n??¨m?????????
                if(count == 0) {
                    String[] array = line.split(" ", 0);
                    n = Integer.parseInt(array[0]);
                    m = Integer.parseInt(array[1]);
                    count++;
                    continue;
                }
                
                // ?????????????????????
                if(nc < n) {
                    String[] row = line.split(" ", 0);
                    for(int i = 0; i < m; i++) {
                       matrix.add(Integer.parseInt(row[i]));
                    }
                    nc++;
                    continue;
                }
                
                // ???????????????????????????
                if(mc < m) {
                    vector.add(Integer.parseInt(line));
                    mc++;
                    if(mc != m) {
                        continue;
                    }
                }
                
                for(int i = 0; i < n; i++) {
                    int ans = 0;
                    for(int j = 0; j < m; j++) {
                        ans += matrix.get(i * (n + 1) + j) * vector.get(j);
                    }
                    System.out.println(ans);
                }
                count = 0;
                nc = 0;
                mc = 0;
            }
            stdReader.close();
        } catch(Exception e) {
            System.out.println(e);
            e.getStackTrace();
            System.exit(-1);
        }
    }
}