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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ITP1_6_D
{
    class Program
    {
        static void Main(string[] args)
        {
            ////////////////////////////////////////////////////////////////////////////////
            // (n×m)の行列A と (m×1)の列ベクトルb の積は(n×1)の列ベクトルc となる
            // (n×1)の列ベクトルc の i番目の要素c-i をそれぞれ1行に出力する

            // 1行目：n(行)、m(列)
            // 2行目以降のn行：行列Aの要素a-ij
            // n行目以降のm行：ベクトルbの要素b-i
            ////////////////////////////////////////////////////////////////////////////////

            // 1行目を読み込み、行列の行数と列数を取得
            string[] rnk1 = Console.ReadLine().Split(' ');                           
            int n = int.Parse(rnk1[0]);
            int m = int.Parse(rnk1[1]);

            //行列A、ベクトルbの入れ物を作る
            int[,] matrixA = new int[n, m];     //要素数がn×mの2次元配列を宣言
            int[] vectorB = new int[m];         //要素数がm×1のベクトルを宣言

            //行列Aに対する処理
            for (int i = 0; i < n; i++)         //n行分繰り返す
            {
                string[] strA = Console.ReadLine().Split(' ');
                for (int j = 0; j < m; j++)     //m列分繰り返す
                {
                    matrixA[i, j] = int.Parse(strA[j]);
                }
            }

            //ベクトルbに対する処理
            for(int i=0; i<m; i++)
            {
                vectorB[i] = int.Parse(Console.ReadLine());
            }

            //答えを出す処理
            int c;
            for (int i = 0; i < n; i++)
            {
                c = 0;
                for (int j = 0; j < m; j++)
                {
                    c += matrixA[i, j] * vectorB[j];
                }
                Console.WriteLine(c.ToString());
            }
        }
    }
}