module union_find_m use, intrinsic :: iso_fortran_env implicit none type union_find integer(int32), allocatable :: par_(:), size_(:) integer(int32) :: setsize_ contains procedure, pass :: init => init_uf procedure, pass :: union => union_uf procedure, pass :: root => root_uf procedure, pass :: same => same_uf procedure, pass :: size => size_uf end type union_find contains subroutine init_uf(this, n) class(union_find), intent(inout) :: this integer(int32) , intent(in) :: n integer(int32) :: i if (allocated(this%par_)) then if (this%setsize_ /= n) then this%setsize_ = n block integer(int32), allocatable :: new_par(:), new_size(:) allocate(new_par(n), new_size(n)) call move_alloc(from = new_par, to = this%par_) call move_alloc(from = new_size, to = this%size_) end block end if else this%setsize_ = n allocate(this%par_(n), this%size_(n)) end if this%par_(:) = [(i, i = 1, n)] this%size_(:) = 1 end subroutine init_uf subroutine union_uf(this, i, j) class(union_find), intent(inout) :: this integer(int32) , intent(in) :: i, j integer(int32) :: x, y x = this%root(i) y = this%root(j) if (x == y) return if (this%size_(x) < this%size_(y)) then this%par_(x) = y this%size_(y) = this%size_(x) + this%size_(y) else this%par_(y) = x this%size_(x) = this%size_(x) + this%size_(y) end if end subroutine union_uf impure recursive integer(int32) function root_uf(this, i) result(res) class(union_find), intent(inout) :: this integer(int32) , intent(in) :: i res = i if (this%par_(res) == res) return this%par_(res) = this%root(this%par_(res)) res = this%par_(res) end function root_uf impure logical function same_uf(this, i, j) class(union_find), intent(inout) :: this integer(int32) , intent(in) :: i, j same_uf = this%root(i) == this%root(j) end function same_uf impure integer(int32) function size_uf(this, i) result(res) class(union_find), intent(inout) :: this integer(int32), intent(in) :: i integer(int32) :: root root = this%root(i) res = this%size_(root) end function size_uf end module union_find_m module modint_m use, intrinsic :: iso_fortran_env implicit none private integer(int64), parameter :: modulo = 998244353 public :: modint public :: assignment(=), operator(+), operator(-), operator(*), operator(/), inv, operator(**), combination type :: modint integer(int64) :: val_ contains procedure, pass :: to_i64 => to_i64_modint end type modint interface modint module procedure :: init_modint_i32, init_modint_i64 end interface modint interface assignment(=) module procedure :: assign_m_from_m, assign_m_from_i32, assign_m_from_i64 end interface assignment(=) interface operator(+) module procedure :: add_m_m, add_i32_m, add_i64_m, add_m_i32, add_m_i64 end interface operator(+) interface operator(-) module procedure :: sub_m_m, sub_i32_m, sub_i64_m, sub_m_i32, sub_m_i64 end interface operator(-) interface operator(*) module procedure :: mul_m_m, mul_i32_m, mul_i64_m, mul_m_i32, mul_m_i64 end interface operator(*) interface inv module procedure :: inv_modint, inv_i32, inv_i64 end interface inv interface operator(/) module procedure :: div_m_m, div_i32_m, div_i64_m, div_m_i32, div_m_i64 end interface operator(/) interface operator(**) module procedure :: pow_m_i32, pow_m_i64 end interface operator(**) interface combination module procedure :: combination_m_m, combination_m_i32, combination_m_i64, combination_i32_m, combination_i64_m end interface combination contains pure integer(int64) function to_i64_modint(mx) result(res) class(modint), intent(in) :: mx res = mx%val_ end function to_i64_modint pure elemental type(modint) function init_modint_i32(x) result(res) integer(int32), intent(in) :: x res = modint(int(x, int64)) end function init_modint_i32 pure elemental type(modint) function init_modint_i64(x) result(res) integer(int64), intent(in) :: x res%val_ = mod(x, modulo) if (res%val_ < 0) res%val_ = res%val_ + modulo end function init_modint_i64 pure subroutine assign_m_from_m(this, x) type(modint), intent(out) :: this type(modint), intent(in) :: x this%val_ = x%val_ end subroutine assign_m_from_m pure subroutine assign_m_from_i32(this, x) type(modint), intent(out) :: this integer(int32), intent(in) :: x this = modint(x) end subroutine assign_m_from_i32 pure subroutine assign_m_from_i64(this, x) type(modint), intent(out) :: this integer(int64), intent(in) :: x this = modint(x) end subroutine assign_m_from_i64 pure type(modint) function add_m_m(mx, my) result(res) type(modint), intent(in) :: mx, my res%val_ = mod(mx%val_ + my%val_, modulo) end function add_m_m pure type(modint) function add_i32_m(x, my) result(res) integer(int32), intent(in) :: x type(modint), intent(in) :: my res = int(x, int64) + my end function add_i32_m pure type(modint) function add_i64_m(x, my) result(res) integer(int64), intent(in) :: x type(modint), intent(in) :: my res = modint(x) + my end function add_i64_m pure type(modint) function add_m_i32(mx, y) result(res) type(modint), intent(in) :: mx integer(int32), intent(in) :: y res = mx + modint(y) end function add_m_i32 pure type(modint) function add_m_i64(mx, y) result(res) type(modint), intent(in) :: mx integer(int64), intent(in) :: y res = mx + modint(y) end function add_m_i64 pure type(modint) function sub_m_m(mx, my) result(res) type(modint), intent(in) :: mx, my res%val_ = mod(mx%val_ - my%val_, modulo) if (res%val_ < 0) res%val_ = res%val_ + modulo end function sub_m_m pure type(modint) function sub_i32_m(x, my) result(res) integer(int32), intent(in) :: x type(modint), intent(in) :: my res = modint(x) - my end function sub_i32_m pure type(modint) function sub_i64_m(x, my) result(res) integer(int64), intent(in) :: x type(modint), intent(in) :: my res = modint(x) - my end function sub_i64_m pure type(modint) function sub_m_i32(mx, y) result(res) type(modint), intent(in) :: mx integer(int32), intent(in) :: y res = mx - modint(y) end function sub_m_i32 pure type(modint) function sub_m_i64(mx, y) result(res) type(modint), intent(in) :: mx integer(int64), intent(in) :: y res = mx - modint(y) end function sub_m_i64 pure type(modint) function mul_m_m(mx, my) result(res) type(modint), intent(in) :: mx, my res%val_ = mod(mx%val_ * my%val_, modulo) end function mul_m_m pure type(modint) function mul_i32_m(x, my) result(res) integer(int32), intent(in) :: x type(modint), intent(in) :: my res = modint(x) * my end function mul_i32_m pure type(modint) function mul_i64_m(x, my) result(res) integer(int64), intent(in) :: x type(modint), intent(in) :: my res = modint(x) * my end function mul_i64_m pure type(modint) function mul_m_i32(mx, y) result(res) type(modint), intent(in) :: mx integer(int32), intent(in) :: y res = mx * modint(y) end function mul_m_i32 pure type(modint) function mul_m_i64(mx, y) result(res) type(modint), intent(in) :: mx integer(int64), intent(in) :: y res = mx * modint(y) end function mul_m_i64 pure type(modint) function inv_modint(mx) result(res) type(modint), intent(in) :: mx integer(int64) :: g, a_inv, y call extend_euclid(mx%val_, modulo, g, a_inv, y) !> if (g /= 1) error stop 1, something wrong... !> g == 1. res = modint(a_inv) end function inv_modint pure type(modint) function inv_i32(x) result(res) integer(int32), intent(in) :: x res = inv_modint(modint(x)) end function inv_i32 pure type(modint) function inv_i64(x) result(res) integer(int64), intent(in) :: x res = inv_modint(modint(x)) end function inv_i64 !> a*x + b*y == g pure subroutine extend_euclid(a, b, g, x, y) integer(int64), intent(in) :: a, b integer(int64), intent(out) :: g, x, y integer(int64) :: q integer(int64) :: zs(0:1), xs(0:1), ys(0:1) integer(int32) :: old, next zs(0) = a; zs(1) = b xs(0) = 1; xs(1) = 0 ys(0) = 0; ys(1) = 1 old = 1 do next = ieor(old, 1) if (zs(old) == 0) exit q = zs(next) / zs(old) zs(next) = zs(next) - q*zs(old) xs(next) = xs(next) - q*xs(old) ys(next) = ys(next) - q*ys(old) old = next end do x = xs(next) y = ys(next) g = a*x + b*y end subroutine extend_euclid pure type(modint) function div_m_m(mx, my) result(res) type(modint), intent(in) :: mx, my res = mx * inv(my) end function div_m_m pure type(modint) function div_i32_m(x, my) result(res) integer(int32), intent(in) :: x type(modint), intent(in) :: my res = modint(x) / my end function div_i32_m pure type(modint) function div_i64_m(x, my) result(res) integer(int64), intent(in) :: x type(modint), intent(in) :: my res = modint(x) / my end function div_i64_m pure type(modint) function div_m_i32(mx, y) result(res) type(modint), intent(in) :: mx integer(int32), intent(in) :: y res = mx / modint(y) end function div_m_i32 pure type(modint) function div_m_i64(mx, y) result(res) type(modint), intent(in) :: mx integer(int64), intent(in) :: y res = mx / modint(y) end function div_m_i64 pure type(modint) function pow_m_i32(mx, p) result(res) type(modint), intent(in) :: mx integer(int32), intent(in) :: p res = mx ** int(p, int64) end function pow_m_i32 pure type(modint) function pow_m_i64(mx, p) result(res) type(modint), intent(in) :: mx integer(int64), intent(in) :: p type(modint) :: mv, mx_powered integer(int64) :: pow mv = 1 mx_powered = mx pow = p do while (pow /= 0) if (iand(pow, b'1') == 1) then mv = mv * mx_powered end if mx_powered = mx_powered * mx_powered pow = ishft(pow, -1) end do res = mv end function pow_m_i64 pure type(modint) function combination_m_m(mn, mr) result(res) type(modint), intent(in) :: mn, mr integer(int64) :: i res = modint(1) do i = 1, mr%to_i64() res = res * (mn%to_i64()-i+1) / i end do end function combination_m_m pure type(modint) function combination_m_i32(mn, r) result(res) type(modint), intent(in) :: mn integer(int32), intent(in) :: r res = combination(mn, modint(r)) end function combination_m_i32 pure type(modint) function combination_m_i64(mn, r) result(res) type(modint), intent(in) :: mn integer(int64), intent(in) :: r res = combination(mn, modint(r)) end function combination_m_i64 pure type(modint) function combination_i32_m(n, mr) result(res) integer(int32), intent(in) :: n type(modint), intent(in) :: mr res = combination(modint(n), mr) end function combination_i32_m pure type(modint) function combination_i64_m(n, mr) result(res) integer(int64), intent(in) :: n type(modint), intent(in) :: mr res = combination(modint(n), mr) end function combination_i64_m end module modint_m program yukicoder_2494 use, intrinsic :: iso_fortran_env use union_find_m use modint_m implicit none integer(int32) :: n, m, u, v integer(int64), allocatable :: arr(:) type(modint) :: ans type(modint), allocatable :: summ(:) type(union_find) :: uf integer(int32) :: i read(input_unit, *) n, m allocate(arr(n)) read(input_unit, *) arr(:) call uf%init(n) do i = 1, m read(input_unit, *) u, v call uf%union(u, v) end do allocate(summ(n), source = modint(0)) ans = modint(1) do i = 1, n summ(uf%root(i)) = summ(uf%root(i)) + arr(i) end do do i = 1, n ans = ans * summ(uf%root(i)) end do write(output_unit, '(i0)') ans end program yukicoder_2494