module math_mod ! This module include ! gcd, lcm ! extgcd use,intrinsic :: iso_fortran_env implicit none integer(int32),parameter:: byte = int64 contains function lcm(a, b) result(ret) integer(byte),intent(in):: a,b integer(byte):: ret ret = a*b/gcd(a,b) end function recursive function gcd(a, b) result(ret) integer(byte),intent(in):: a,b integer(byte):: ret if (b == 0_byte) then ret = a else ret = gcd(b, mod(a,b)) end if end function recursive function extgcd(a, b, x, y) result(ret) ! solve:: ax + by = gcd(a,b) ! input:: a, b ! output:: x, y, gcd(a,b) integer(byte),value:: a,b integer(byte),intent(out):: x,y integer(byte):: ret ! gcd(a,b) if (b==0_byte) then ret = a x = 1_byte y = 0_byte else ret = extgcd(b, mod(a,b), y, x) y = y - a/b * x end if end function recursive function mod_inv(a,m) result(ret) ! solve:: mod(ax, m) = 1 ! => ax + my = 1 ! input:: a,m ! output:: x <- モジュラ逆数 integer(byte),intent(in):: a,m integer(byte):: ret, gcd_ma, x, y gcd_ma = extgcd(a,m,x,y) if (gcd_ma /= 1_byte) then ret = -1_byte else ret = modulo(x,m) end if end function function chineserem(b, m, md) result(ret) ! solve:: mod(b_1*k_1, m_1) = x ! : ! mod(b_n*k_n, m_n) = x を満たす最小のx ! input:: b(1:n), m(1:n) ! output:: x%md integer(byte),allocatable:: b(:),m(:) integer(byte):: md integer(byte),allocatable:: x0(:), mmul(:) integer(byte):: ret, i, j, g, gi, gj integer(byte):: t do i=1_byte,size(b) do j=1_byte, i-1_byte g = gcd(m(i),m(j)) if (mod(b(i)-b(j), g) /= 0_byte) then ret = -1_byte return end if m(i) = m(i) / g m(j) = m(j) / g gi = gcd(m(i),g) gj = g/gi do while(g /= 1) g = gcd(gi,gj) gi = gi*g gj = gj/g end do m(i) = m(i)*gi m(j) = m(j)*gj b(i) = mod(b(i), m(i)) b(j) = mod(b(j), m(j)) ! print'(*(i0,1x))', i, j, m(i), m(j), b(i), b(j) end do end do ! print*, "b", b(:) ! print*, "m", m(:) m = [m,md] allocate(x0(size(m)), source=0_byte) allocate(mmul(size(m)), source=1_byte) do i=1_byte,size(b) t = modulo((b(i)-x0(i)) * mod_inv(mmul(i), m(i)), m(i)) do j=i+1,size(m) x0(j) = modulo(x0(j) + t * mmul(j), m(j)) mmul(j) = modulo(mmul(j)*m(i), m(j)) end do end do ! print*, x, mmul ret = modulo(x0(size(x0)), md) end function end module program main use,intrinsic :: iso_fortran_env use math_mod implicit none integer(int64):: n, i, md=10_int64**9+7, lcmv, sumx, ans integer(int64),allocatable:: x(:), y(:) read*, n allocate(x(n), y(n)) read*, (x(i), y(i), i=1,n) sumx=0 lcmv=1 do i=1,n sumx = modulo(sumx + x(i), md) end do ans = chineserem(x,y,md) if (sumx == 0) then ! print*, 'a' do i=1,n lcmv = mod(lcmv*y(i), md) end do print'(i0)', lcmv else print'(i0)', ans end if end program main