static private void checkMul(ModMatrix a, ModMatrix b)
{
if (a.col != b.row)
{
throw new Exception("row and col have to be same.");
}
}
public override IEnumerable <object> Solve(TextReader inputStream)
{
var(n, k) = inputStream.ReadValue <int, long>();
var initialVector = new ModVector(Enumerable.Repeat(Modular.One, n).ToArray());
var matrix = new ModMatrix(n);
for (int i = 0; i < n; i++)
{
var a = inputStream.ReadIntArray();
for (int j = 0; j < n; j++)
{
matrix[i, j] = a[j];
}
}
var resultVector = matrix.Pow(k) * initialVector;
var result = Modular.Zero;
for (int i = 0; i < resultVector.Length; i++)
{
result += resultVector[i];
}
yield return(result);
}
static void Main()
{
var n = long.Parse(Console.ReadLine());
var morning = new ModMatrix(3, 3);
var other = new ModMatrix(3, 3);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
if (i == j)
{
continue;
}
if (i != 2)
{
morning[i, j] = 1;
}
other[i, j] = 1;
}
}
var iv = new ModMatrix(3, 1);
iv[0, 0] = 1;
iv[1, 0] = 1;
var last = Power(other * other * morning, n - 1) * (other * other * iv);
Console.WriteLine((last[0, 0] + last[1, 0] + last[2, 0]) % 1000000007);
}
public void Solve()
{
var a = sc.Long();
var b = sc.Long();
ModInteger.Mod = sc.Integer();
var mat = new ModMatrix(2, 2);
mat[0, 0] = 10;
mat[0, 1] = 1;
mat[1, 1] = 1;
var vec = new ModMatrix(2, 1);
vec[0, 0] = 1;
vec[0, 1] = 1;
var gcd = MathEx.GCD(a, b);
var A = (ModMatrix.Pow(mat, a - 1) * vec)[0, 0];
mat[0, 0] = ModInteger.Pow(10, gcd);
var B = (ModMatrix.Pow(mat, b / gcd - 1) * vec)[0, 0];
IO.Printer.Out.WriteLine(A * B);
//IO.Printer.Out.WriteLine(A * B * ModInteger.Inverse(GCD));
}
static void Main()
{
var l = Read();
var a = Read();
var b = Read();
var m = (int)Read();
ModMatrix.MOD = m;
ModInt.MOD = m;
long lastRem = 0;
long n = 0;
for (int digits = GetDigits(a); digits < 40; digits++)
{
ModMatrix matrix = new ModMatrix(3, 3);
matrix[0, 0] = Power(10, digits);
matrix[0, 1] = b;
matrix[0, 2] = a;
matrix[1, 1] = 1;
matrix[1, 2] = 1;
matrix[2, 2] = 1;
ModMatrix iv = new ModMatrix(3, 1);
iv[0, 0] = lastRem;
iv[1, 0] = n;
iv[2, 0] = 1;
BigInteger valid = n - 1;
BigInteger invalid = new BigInteger(long.MaxValue) * 1000000;
while (invalid - valid > 1)
{
var mid = (valid + invalid) / 2;
if (GetDigits(a + b * mid) == digits)
{
valid = mid;
}
else
{
invalid = mid;
}
}
if (l - 1 <= valid)
{
valid = l - 1;
}
var count = (long)valid - n + 1;
var resMatrix = Power(matrix, count) * iv;
lastRem = resMatrix[0, 0];
n = (long)valid + 1;
if (valid == l - 1)
{
break;
}
}
Console.WriteLine(lastRem);
}
public Voice(double samplerate, int bufferSize)
{
this.samplerate = samplerate;
bufsize = bufferSize;
ampEnvBuffer = new double[bufsize];
filter1EnvBuffer = new double[bufsize];
filter2EnvBuffer = new double[bufsize];
path1Buffer = new double[bufsize];
path2Buffer = new double[bufsize];
processBuffer = new double[bufsize];
OutputBuffer = new double[2][];
OutputBuffer[0] = new double[48000];
OutputBuffer[1] = new double[48000];
Modules = new Dictionary <ModuleId, object>();
Osc1 = new MultiOsc(samplerate, bufsize);
Osc2 = new BlOsc(samplerate, bufsize);
Osc3 = new BlOsc(samplerate, bufsize);
Osc4 = new BlOsc(samplerate, bufsize);
//Ins1 = new InsRedux(samplerate, Bufsize);
//Ins2 = new InsRedux(samplerate, Bufsize);
Ins1 = new InsDistortion(samplerate, bufsize);
Ins2 = new InsDistortion(samplerate, bufsize);
Filter1 = new DualFilter(samplerate, bufsize);
Filter2 = new DualFilter(samplerate, bufsize);
AmpEnv = new Ahdsr(samplerate);
Filter1Env = new Ahdsr(samplerate);
Filter2Env = new Ahdsr(samplerate);
Mod1 = new Modulator(samplerate);
Mod2 = new Modulator(samplerate);
Mod3 = new Modulator(samplerate);
Mod4 = new Modulator(samplerate);
Mod5 = new Modulator(samplerate);
Mod6 = new Modulator(samplerate);
MidiInput = new MidiInput();
ModMatrix = new ModMatrix(this);
Mixer = new Mixer();
RefreshModuleObjects();
Mod1.UpdateStepsize();
Mod2.UpdateStepsize();
Mod3.UpdateStepsize();
Mod4.UpdateStepsize();
Mod5.UpdateStepsize();
Mod6.UpdateStepsize();
Mixer.Update();
}
public static ModMatrix[] PowTable(ModMatrix m, int k)
{
var ret = new ModMatrix[k];
ret[0] = m;
for (int i = 1; i < k; i++)
{
ret[i] = ret[i - 1] * ret[i - 1];
}
return(ret);
}
public static ModMatrix Trans(ModMatrix m)
{
var ret = new ModMatrix(m.col, m.row);
for (int i = 0; i < m.row; i++)
{
for (int j = 0; j < m.col; j++)
{
ret.mat[j * m.col + i] = m.mat[i * m.col + j];
}
}
return(ret);
}
public static ModMatrix operator +(ModMatrix l, ModMatrix r)
{
check(l, r);
var ret = new ModMatrix(l.row, l.col);
for (int i = 0; i < l.row; i++)
{
for (int j = 0; j < l.col; j++)
{
ret.mat[i * ret.col + j] = l.mat[i * l.col + j] + r.mat[i * r.col + j];
}
}
return(ret);
}
static ModMatrix Power(ModMatrix n, long m)
{
ModMatrix pow = n;
ModMatrix res = ModMatrix.GetScalarMatrix(n.Height, 1);
while (m > 0)
{
if ((m & 1) == 1)
{
res *= pow;
}
pow *= pow;
m >>= 1;
}
return(res);
}
public static ModMatrix operator *(ModMatrix l, ModMatrix r)
{
checkMul(l, r);
var ret = new ModMatrix(l.row, r.col);
for (int i = 0; i < l.row; i++)
{
for (int k = 0; k < l.col; k++)
{
for (int j = 0; j < r.col; j++)
{
ret.mat[i * r.col + j] = (ret.mat[i * r.col + j] + l.mat[i * l.col + k] * r.mat[k * r.col + j]);
}
}
}
return(ret);
}
public static ModMatrix PowWithTable(ModMatrix m, long n, ModMatrix[] table)
{
var ret = new ModMatrix(m.row, m.col);
for (int i = 0; i < m.row; i++)
{
ret.mat[i * m.col + i] = 1;
}
for (int i = 0; i < table.Length; i++)
{
if ((n & 1) == 1)
{
ret = ret * table[i];
}
}
return(ret);
}
public static ModMatrix Pow(ModMatrix m, long n)
{
var ret = new ModMatrix(m.row, m.col);
for (int i = 0; i < m.row; i++)
{
ret.mat[i * m.col + i] = 1;
}
for (; n > 0; m *= m, n >>= 1)
{
if ((n & 1) == 1)
{
ret = ret * m;
}
}
return(ret);
}
public static ModMatrix Multiple(ModMatrix a, ModMatrix b)
{
Debug.Assert(a.Width == b.Height);
var res = new ModMatrix(a.Height, b.Width);
for (int i = 0; i < a.Height; i++)
{
for (int j = 0; j < b.Width; j++)
{
for (int k = 0; k < a.Width; k++)
{
res[i, j] += a[i, k] * b[k, j];
res[i, j] %= MOD;
}
}
}
return(res);
}
static ModMatrix Power(ModMatrix n, long m)
{
ModMatrix pow = n;
ModMatrix res = new ModMatrix(n.Height, n.Width);
for (int i = 0; i < n.Height; i++)
{
res[i, i] = 1;
}
while (m > 0)
{
if ((m & 1) == 1)
{
res *= pow;
}
pow *= pow;
m >>= 1;
}
return(res);
}
public void Execute()
{
ProgressChanged(0, 1);
if (!CheckParameters())
{
return;
}
if (!settings.Action)
{
mat = inv; // decrypt
}
GuiLogMessage("The matrix is " + mat, NotificationLevel.Debug);
Output = "";
BigInteger[] result, vector = new BigInteger[mat.Dimension];
for (int j = 0; j < Input.Length; j += mat.Dimension)
{
for (int k = 0; k < mat.Dimension; k++)
{
vector[k] = settings.Alphabet.IndexOf(Input[j + k]);
}
result = mat * vector;
for (int k = 0; k < mat.Dimension; k++)
{
Output += settings.Alphabet[(int)result[k]];
}
}
OnPropertyChanged("Output");
ProgressChanged(1, 1);
}
static void Main()
{
int n = int.Parse(Console.ReadLine());
//matrix[i,j]:vector[i]????a????i???j???a????????(DP??????)
ModMatrix matrix = new ModMatrix(4 * 4 * 4, 4 * 4 * 4);
//t : 0
//a : 1
//g : 2
//c : 3
for (int i = 0; i < matrix.Height; i++)
{
int val = i;
//t s f
int firstLiteral = val % 4;
val /= 4;
int secondLiteral = val % 4;
val /= 4;
int thirdLiteral = val % 4;
//?????agc,gac,acg,a_gc,ag_c
//t???????
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 0] += 1;
//a???????
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 1] += 1;
//g???????:acg??????
if (!(secondLiteral == 1 && firstLiteral == 3 /*acg*/))
{
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 2] += 1;
}
//c??????? : agc,gac,a_gc,ag_c??????
if (!(secondLiteral == 1 && firstLiteral == 2 /*agc*/) &&
!(secondLiteral == 2 && firstLiteral == 1 /*gac*/) &&
!(thirdLiteral == 1 && firstLiteral == 2 /*a_gc*/) &&
!(thirdLiteral == 1 && secondLiteral == 2 /*ag_c*/))
{
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 3] += 1;
}
}
ModMatrix res = new ModMatrix(1, 4 * 4 * 4);
res[0, 0] = 1;
while (n > 0)
{
if ((n & 1) == 1)
{
res *= matrix;
}
matrix *= matrix;
n >>= 1;
}
long resSum = 0;
for (int i = 0; i < res.Width; i++)
{
resSum += res[0, i];
}
Console.WriteLine(resSum % 1000000007);
}
static void Main()
{
//matrix[i,j]:vector[i]の要素が1であればi行目のj要素に乗算が行われ、そこに遷移する
var nk = Console.ReadLine().Split().Select(int.Parse).ToArray();
int n = nk[0];
int k = nk[1];
ModMatrix matrix = new ModMatrix(k * k * k, k * k * k);
//k=2の時
// a : 01010101
// ab : 00110011
//abc : 00001111
for (int i = 0; i < matrix.Height; i++)
{
int val = i;
int aCount = val % k;
val /= k;
int abCount = val % k;
val /= k;
int abcCount = val % k;
int newACount, newABCount, newABCCount;
//aが追加された時
newACount = (aCount + 1) % k;
newABCount = abCount;
newABCCount = abcCount;
matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1;
//bが追加された時
newACount = aCount;
newABCount = (abCount + aCount) % k;
newABCCount = abcCount;
matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1;
//cが追加された時
newACount = aCount;
newABCount = abCount;
newABCCount = (abcCount + abCount) % k;
matrix[i, (newABCCount * k + newABCount) * k + newACount] += 1;
}
ModMatrix res = new ModMatrix(1, k * k * k);
res[0, 0] = 1;
long pow = n;
while (n > 0)
{
if ((n & 1) == 1)
{
res *= matrix;
}
matrix *= matrix;
n >>= 1;
}
long resSum = 0;
for (int i = 0; i < k * k; i++)
{
resSum += res[0, i];
}
Console.WriteLine(resSum % 998244353);
}
static void Main()
{
int n = int.Parse(Console.ReadLine());
//matrix[i,j]:vector[i]の要素がaであればi行目のj要素にaで乗算が行われる(DPの遷移と同じ)
ModMatrix matrix = new ModMatrix(4 * 4 * 4, 4 * 4 * 4);
//t : 0
//a : 1
//g : 2
//c : 3
for (int i = 0; i < matrix.Height; i++)
{
int val = i;
//t s f
int firstLiteral = val % 4;
val /= 4;
int secondLiteral = val % 4;
val /= 4;
int thirdLiteral = val % 4;
//ダメなのはagc,gac,acg,a_gc,ag_c
//tが追加された時
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 0] += 1;
//aが追加された時
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 1] += 1;
//gが追加された時:acgが起こりうる
if (!(secondLiteral == 1 && firstLiteral == 3 /*acg*/))
{
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 2] += 1;
}
//cが追加された時 : agc,gac,a_gc,ag_cが起こりうる
if (!(secondLiteral == 1 && firstLiteral == 2 /*agc*/) &&
!(secondLiteral == 2 && firstLiteral == 1 /*gac*/) &&
!(thirdLiteral == 1 && firstLiteral == 2 /*a_gc*/) &&
!(thirdLiteral == 1 && secondLiteral == 2 /*ag_c*/))
{
matrix[i, (secondLiteral * 4 + firstLiteral) * 4 + 3] += 1;
}
}
ModMatrix res = new ModMatrix(1, 4 * 4 * 4);
res[0, 0] = 1;
while (n > 0)
{
if ((n & 1) == 1)
{
res *= matrix;
}
matrix *= matrix;
n >>= 1;
}
long resSum = 0;
for (int i = 0; i < res.Width; i++)
{
resSum += res[0, i];
}
Console.WriteLine(resSum % 1000000007);
}
private bool CheckParameters()
{
int dim;
string[] s = null;
BigInteger[] matelements;
if (Matrix == null)
{
// get matrix from settings
s = settings.MatrixString.Split(',');
dim = (int)Math.Sqrt(s.Length);
matelements = new BigInteger[dim];
}
else
{
// get matrix from matrix input
matelements = Matrix;
dim = (int)Math.Sqrt(Matrix.Length);
}
if (dim < 1)
{
GuiLogMessage("The dimension of the matrix must be greater than 0!", NotificationLevel.Error);
return(false);
}
if (dim * dim != Matrix.Length)
{
GuiLogMessage("The number of elements in the matrix definition must be a square number!", NotificationLevel.Error);
return(false);
}
if (settings.Modulus < 2)
{
GuiLogMessage(String.Format("The input alphabet must contain at least 2 different characters!"), NotificationLevel.Error);
return(false);
}
if (Input.Length % dim != 0)
{
GuiLogMessage(String.Format("The input was padded so that its length is a multiple of the matrix dimension ({0})!", dim), NotificationLevel.Warning);
char paddingChar = settings.Alphabet.Contains("X") ? 'X' : (settings.Alphabet.Contains("x") ? 'x' : settings.Alphabet[settings.Modulus - 1]);
Input += new String(paddingChar, dim - (Input.Length % dim));
}
for (int j = 0; j < Input.Length; j++)
{
if (settings.Alphabet.IndexOf(Input[j]) < 0)
{
GuiLogMessage(String.Format("The input contains the illegal character '{0}' at position {1}!", Input[j], j), NotificationLevel.Error);
return(false);
}
}
if (Matrix == null)
{
// read the matrix from the settings string
int i = 0;
try
{
for (i = 0; i < dim; i++)
{
matelements[i] = BigInteger.Parse(s[i]);
}
}
catch (Exception ex)
{
GuiLogMessage(string.Format("Error while parsing matrix element {0}: \"{1}\"!", i, s[i]), NotificationLevel.Error);
return(false);
}
}
mat = new ModMatrix(dim, settings.Modulus);
int k = -1;
for (int y = 0; y < mat.Dimension; y++)
{
for (int x = 0; x < mat.Dimension; x++)
{
mat[x, y] = matelements[++k];
}
}
inv = mat.invert();
if (inv == null)
{
GuiLogMessage("The matrix " + mat + " is not invertible.", NotificationLevel.Error);
return(false);
}
return(true);
}
