using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static string InputPattern = "InputX";
static List<string> GetInputList()
{
var WillReturn = new List<string>();
if (InputPattern == "Input1") {
WillReturn.Add("10 2");
WillReturn.Add("0 1");
WillReturn.Add("1 0");
//512
}
else if (InputPattern == "Input2") {
WillReturn.Add("2 5");
WillReturn.Add("0 1 1 1 1");
WillReturn.Add("1 0 1 1 1");
WillReturn.Add("1 1 0 1 1");
WillReturn.Add("1 1 1 0 1");
WillReturn.Add("1 1 1 1 0");
//1025
}
else {
string wkStr;
while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
}
return WillReturn;
}
const long Hou = 1000000007;
static long mH;
static long mR;
static long[,] mEdgeArr;
static long UB;
static void Main()
{
List<string> InputList = GetInputList();
long[] wkArr = InputList[0].Split(' ').Select(pX => long.Parse(pX)).ToArray();
mH = wkArr[0];
mR = wkArr[1];
mEdgeArr = CreateBanArr(InputList.Skip(1));
UB = mEdgeArr.GetUpperBound(0);
long Result = Solve();
Console.WriteLine(Result);
}
static long Solve()
{
// 1階しかない場合
if (mH == 1) return 1;
// 場合の数 [開始ノード,終点ノード] な配列
long[,] PatternArr = new long[UB + 1, UB + 1];
for (long I = 0; I <= UB; I++) {
long[,] TSPResult = ExecTSP(I);
for (long J = 0; J <= TSPResult.GetUpperBound(0); J++) {
for (long K = 0; K <= TSPResult.GetUpperBound(1); K++) {
PatternArr[I, J] += TSPResult[J, K];
}
}
}
long[,] FirstMatrix = new long[UB + 1, UB + 1];
for (long I = 0; I <= UB; I++) {
FirstMatrix[0, I] = PatternArr[0, I];
}
long[,] LastMatrix = new long[UB + 1, UB + 1];
for (long I = 0; I <= UB; I++) {
LastMatrix[I, 0] = PatternArr[I, 0];
}
// 行列の積は、結合法則が成り立つので、最初と最後以外は、繰り返し二乗法を使う
long[,] BekijyouMatrix = DeriveBekijyouMatrix(PatternArr, mH - 2);
long[,] AnswerMatrix = DeriveMatrixProd(FirstMatrix, BekijyouMatrix);
AnswerMatrix = DeriveMatrixProd(AnswerMatrix, LastMatrix);
long Answer = 0;
for (long I = 0; I <= UB; I++) {
Answer += AnswerMatrix[I, 0];
Answer %= Hou;
}
return Answer;
}
// 始点ノードを引数として、場合の数 [現在ノード , 訪問済ノードセット] な配列を返す
static long[,] ExecTSP(long pStaNode)
{
long AllBitOn = (1 << (int)mR) - 1;
// 場合の数 [現在ノード , 訪問済ノードセット] なDP表
long[,] PrevDP = new long[UB + 1, AllBitOn + 1];
PrevDP[pStaNode, 1 << (int)pStaNode] = 1;
long[,] WillReturn = new long[UB + 1, AllBitOn + 1];
WillReturn[pStaNode, 1 << (int)pStaNode] = 1;
for (long I = 1; I <= mR - 1; I++) { // 移動回数でループ
long[,] CurrDP = new long[UB + 1, AllBitOn + 1];
for (long J = 0; J <= UB; J++) {
for (long K = 0; K <= AllBitOn; K++) {
if (PrevDP[J, K] == 0) continue;
for (long L = 0; L <= UB; L++) { // 移動先ノード
if (mEdgeArr[J, L] == 0) continue;
// ビットシフトする必要あり
long LBit = (1 << (int)L);
// 再訪は不可
if ((K & LBit) > 0) continue;
long NewJ = L;
long NewK = K | LBit;
CurrDP[NewJ, NewK] += PrevDP[J, K];
CurrDP[NewJ, NewK] %= Hou;
WillReturn[NewJ, NewK] += PrevDP[J, K];
WillReturn[NewJ, NewK] %= Hou;
}
}
}
PrevDP = CurrDP;
}
return WillReturn;
}
// 正方行列2つの積を返す
static long[,] DeriveMatrixProd(long[,] pMatrix1, long[,] pMatrix2)
{
long UB = pMatrix1.GetUpperBound(0);
// 横の値の配列[行]
var YokoArrDict = new Dictionary<long, long[]>();
for (long LoopY = 0; LoopY <= UB; LoopY++) {
var YokoList = new List<long>();
for (long LoopX = 0; LoopX <= UB; LoopX++) {
YokoList.Add(pMatrix1[LoopY, LoopX] % Hou);
}
YokoArrDict[LoopY] = YokoList.ToArray();
}
// 縦の値の配列[列]
var TateArrDict = new Dictionary<long, long[]>();
for (long LoopX = 0; LoopX <= UB; LoopX++) {
var TateList = new List<long>();
for (long LoopY = 0; LoopY <= UB; LoopY++) {
TateList.Add(pMatrix2[LoopY, LoopX] % Hou);
}
TateArrDict[LoopX] = TateList.ToArray();
}
long[,] MatrixProd = new long[UB + 1, UB + 1];
for (long LoopY = 0; LoopY <= UB; LoopY++) {
for (long LoopX = 0; LoopX <= UB; LoopX++) {
long SumVal = 0;
for (long K = 0; K <= UB; K++) {
SumVal += (YokoArrDict[LoopY][K] * TateArrDict[LoopX][K] % Hou) % Hou;
SumVal %= Hou;
}
MatrixProd[LoopY, LoopX] = SumVal;
}
}
return MatrixProd;
}
// 正方行列のP乗を、繰り返し2乗法で求める
static long[,] DeriveBekijyouMatrix(long[,] pBaseMatrix, long pP)
{
long[,] CurrJyousuu = (long[,])pBaseMatrix.Clone();
long CurrShisuu = 1;
long[,] WillReturn = DeriveUnitMatrix(pBaseMatrix.GetUpperBound(0));
while (true) {
// 対象ビットが立っている場合
if ((pP & CurrShisuu) > 0) {
WillReturn = DeriveMatrixProd(WillReturn, CurrJyousuu);
}
CurrShisuu *= 2;
if (CurrShisuu > pP) return WillReturn;
CurrJyousuu = DeriveMatrixProd(CurrJyousuu, CurrJyousuu);
}
}
// 単位行列を返す
static long[,] DeriveUnitMatrix(long UB)
{
long[,] WillReturn = new long[UB + 1, UB + 1];
for (long LoopY = 0; LoopY <= UB; LoopY++) {
for (long LoopX = 0; LoopX <= UB; LoopX++) {
if (LoopY == LoopX) {
WillReturn[LoopY, LoopX] = 1;
}
}
}
return WillReturn;
}
////////////////////////////////////////////////////////////////
// IEnumerable<string>をlongの2次元配列に設定する
////////////////////////////////////////////////////////////////
static long[,] CreateBanArr(IEnumerable<string> pStrEnum)
{
var StrList = pStrEnum.ToList();
if (StrList.Count == 0) {
return new long[0, 0];
}
long[] IntArr = { };
Action<string> SplitAct = pStr =>
IntArr = pStr.Split(' ').Select(pX => long.Parse(pX)).ToArray();
SplitAct(StrList[0]);
long UB_X = IntArr.GetUpperBound(0);
long UB_Y = StrList.Count - 1;
long[,] WillReturn = new long[UB_X + 1, UB_Y + 1];
for (long Y = 0; Y <= UB_Y; Y++) {
SplitAct(StrList[(int)Y]);
for (long X = 0; X <= UB_X; X++) {
WillReturn[X, Y] = IntArr[X];
}
}
return WillReturn;
}
}