module algorithm_md
contains
    recursive subroutine qsort(a,s,t)
        implicit none
        integer*8::a(:),m
        integer::s,t,i,j
        if(t-s<=1)return
        i=s
        j=t-1
        m=a((s+t)/2)
        do
            do while(a(i)<m)
                i=i+1
            end do
            do while(a(j)>m)
                j=j-1
            end do
            if(i>=j)exit
            a(i)=xor(a(i),a(j))
            a(j)=xor(a(i),a(j))
            a(i)=xor(a(i),a(j))
            i=i+1
            j=j-1
        end do
        call qsort(a,s,i)
        call qsort(a,j+1,t)
    end subroutine

    function binarysearch(a,v)
        integer*8::a(:),v
        integer::ok,ng,middle,binarysearch
        ok=1
        ng=size(a)+1
        do while(ng-ok>1)
            middle=(ok+ng)/2
            if(a(middle)<=v)then
                ok=middle
            else
                ng=middle
            end if
        end do
        binarysearch=ok
        if(a(ok)/=v)then
            print*,"err"
            call  exit(1)
        end if
    end function

end module
module djset_md
    private
    type,public::DJSet
        integer::n
        integer*8::ans=0
        integer,allocatable::upper(:)
        integer*8,allocatable::mi(:),ma(:),top(:)
    contains
        procedure::build=>build_
        procedure::root=>root_
        procedure::setUnion=>setUnion_
        procedure::equiv=>equiv_
        procedure::confluentUnion=>confluentUnion_
    end type

contains
    subroutine build_(o,n_)
        implicit none
        integer::i,j,k
        class(DJSet)::o
        integer::n_
        o%n=n_
        allocate(o%upper(o%n))
        allocate(o%ma(o%n))
        allocate(o%mi(o%n))
        allocate(o%top(o%n))
        do i=1,o%n
            o%upper(i)=-1
            o%top(i)=i
        end do
    end subroutine

    recursive function root_(o,x)result(res)
        implicit none
        class(DJSet)::o
        integer::x,res
        if(o%upper(x)<0)then
            res=x
        else
            o%upper(x)=o%root(o%upper(x))
            res=o%upper(x)
        end if
    end function

    subroutine confluentUnion_(o,x,y)
        implicit none
        class(DJSet)::o
        integer::x,y,middle
        if(x>y)then
            x=xor(x,y)
            y=xor(x,y)
            x=xor(x,y)
        end if
        do while(.not.o%equiv(x,y))
            !x<y
            middle=o%top(x)+1
            call o%setUnion(x,middle)
            x=middle
        end do
    end subroutine

    subroutine setUnion_(o,x,y)
        implicit none
        class(DJSet)::o
        integer::x,y
        x=root_(o,x)
        y=root_(o,y)
        if(x==y)return
        if(o%upper(x)<o%upper(y))then
            x=xor(x,y)
            y=xor(x,y)
            x=xor(x,y)
        end if
        o%upper(y)=o%upper(x)+o%upper(y)
        o%upper(x)=y
        o%ma(y)=max(o%ma(x),o%ma(y))
        o%mi(y)=min(o%mi(x),o%mi(y))
        o%top(y)=max(o%top(x),o%top(y))
        o%ans=max(o%ans,o%ma(y)-o%mi(y))
    end subroutine


    function equiv_(o,x,y)
        implicit none
        class(DJSet)::o
        integer::x,y
        logical::equiv_
        equiv_=o%root(x)==o%root(y)
    end function
end module

program main
    use algorithm_md
    use djset_md
    implicit none
    integer*8::D,Q
    integer::i,j,k
    integer*8,allocatable::a(:),b(:),tmp_arr(:)
    type(DJSet)::ds
    read(*,*)D,Q
    allocate(a(Q))
    allocate(b(Q))
    allocate(tmp_arr(2*Q))
    do i=1,Q
        read(*,*)a(i),b(i)
        tmp_arr(i)=a(i)
        tmp_arr(i+Q)=b(i)+1
    end do
    call qsort(tmp_arr,1,size(tmp_arr)+1)
    j=1
    do i=1,size(tmp_arr)
        if(i+1<=size(tmp_arr).and.tmp_arr(i)==tmp_arr(i+1))cycle
        tmp_arr(j)=tmp_arr(i)
        j=j+1
    end do
    tmp_arr=tmp_arr(1:j-1)
    call ds%build(j-1)
    do i=1,j-1
        ds%ma(i)=tmp_arr(i)
        ds%mi(i)=tmp_arr(i)
    end do
    do i=1,Q
        call ds%confluentUnion(binarysearch(tmp_arr,a(i)),binarysearch(tmp_arr,b(i)+1))
        print*,ds%ans
    end do
end program