import algorithm, macros, math, sequtils, strutils, tables # import bitops, lenientops, deques, # heapqueue, sets, sugar let read* = iterator: string = while true: (for s in stdin.readLine.split: yield s) template input*(T: static[typedesc]): untyped = when T is int: read().parseInt elif T is float: read().parseFloat elif T is string: read() elif T is char: read()[0] macro dump*(args: varargs[typed]): untyped = result = newNimNode(nnkStmtList) for x in args: let s = toStrLit(x) result.add quote do: stderr.write `s`, " = ", `x`, " " result.add quote do: stderr.write "\n" proc `|=`*(n: var int, m: int) = n = n or m proc `|=`*(n: var bool, m: bool) = n = n or m proc `&=`*(n: var int, m: int) = n = n and m proc `&=`*(n: var bool, m: bool) = n = n and m proc `^=`*(n: var int, m: int) = n = n xor m proc `^=`*(n: var bool, m: bool) = n = n xor m proc `%=`*(n: var int, m: int) = n = n mod m proc `/=`*(n: var int, m: int) = n = n div m proc `<<=`*(n: var int, m: int) = n = n shl m proc `>>=`*(n: var int, m: int) = n = n shr m proc `?=`*(n: var SomeNumber, m: SomeNumber) = n = max(n, m) proc newSeq2*[T](n1, n2: Natural): seq[seq[T]] = newSeqWith(n1, newSeq[T](n2)) proc newSeq3*[T](n1, n2, n3: Natural): seq[seq[seq[T]]] = newSeqWith(n1, newSeqWith(n2, newSeq[T](n3))) proc newSeq4*[T](n1, n2, n3, n4: Natural): seq[seq[seq[seq[T]]]] = newSeqWith(n1, newSeqWith(n2, newSeqWith(n3, newSeq[T](n4)))) # -------------------------------------------------- # const modulus = 10 ^ 9 + 7 type ModMatrix* = seq[seq[int]] proc initModMatrix*(N: Natural, M: Natural): ModMatrix = ModMatrix(newSeqWith(N, newSeq[int](M))) proc initModMatrix*(N: Natural): ModMatrix = ModMatrix(newSeqWith(N, newSeq[int](N))) proc initIdentityModMatrix*(N: Natural): ModMatrix = var R = initModMatrix(N) for i in 0 .. N - 1: R[i][i] = 1 return R proc toModMatrix*(A: seq[seq[int]]): ModMatrix = A proc height*(A: ModMatrix): Natural {.inline.} = A.len proc width*(A: ModMatrix): Natural {.inline.} = A[0].len proc `+`*(A: ModMatrix, B: ModMatrix): ModMatrix = #assert height(A) == height(B) #assert width(A) == width(B) let (N, M) = (height(A), width(A)) var R = initModMatrix(N, M) for i in 0 .. N - 1: for j in 0 .. M - 1: R[i][j] = A[i][j] + B[i][j] if R[i][j] >= modulus: R[i][j] -= modulus return R proc `-`*(A: ModMatrix, B: ModMatrix): ModMatrix = #assert height(A) == height(B) #assert width(A) == width(B) let (N, M) = (height(A), width(A)) var R = initModMatrix(N, M) for i in 0 .. N - 1: for j in 0 .. M - 1: R[i][j] = A[i][j] - B[i][j] if R[i][j] < 0: R[i][j] += modulus return R proc `*`*(A: ModMatrix, B: ModMatrix): ModMatrix = #assert width(A) == height(B) let (N, P, M) = (height(A), width(A), width(B)) var R = initModMatrix(N, M) for i in 0 .. N - 1: for j in 0 .. M - 1: for k in 0 .. P - 1: R[i][j] += A[i][k] * B[k][j] R[i][j] = R[i][j] mod modulus return R proc `^`*(A: ModMatrix, k: Natural): ModMatrix = #assert height(A) == width(A) let N = height(A) var (A, k, R) = (A, k, initIdentityModMatrix(N)) while k > 0: if bool(k and 1): R = R * A A = A * A k = k shr 1 return R proc `+=`*(A: var ModMatrix, B: ModMatrix) {.inline.} = A = A + B proc `-=`*(A: var ModMatrix, B: ModMatrix) {.inline.} = A = A - B proc `*=`*(A: var ModMatrix, B: ModMatrix) {.inline.} = A = A * B proc `^=`*(A: var ModMatrix, k: Natural) {.inline.} = A = A ^ k # -------------------------------------------------- # let M, K = input(int) var A = initModMatrix(M, M) for j in 0 .. M - 1: for k in 0 .. M - 1: A[(j + k) mod M][j] += 1 A[(j * k) mod M][j] += 1 A ^= K var B = initModMatrix(M, 1); B[0][0] = 1 let R = A * B echo R[0][0]