#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1};
const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1};
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=n;i--;)
#define rrep2(i,n) for(ll i=n;i--;)
#define rrep3(i,a,b) for(ll i=b;i-->(a);)
#define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each1(i,a) for(auto&&i:a)
#define each2(x,y,a) for(auto&&[x,y]:a)
#define each3(x,y,z,a) for(auto&&[x,y,z]:a)
#define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define Msum(...) accumulate(all(__VA_ARGS__),0_M)
#define elif else if
#define unless(a) if(!(a))
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; }
vector<ll> iota(ll n){ vector<ll> a(n); iota(a.begin(), a.end(), 0); return a; }
vector<pll> factor(ull x){ vector<pll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
map<ll,ll> factor_map(ull x){ map<ll,ll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; }
vector<ll> divisor(ull x){ vector<ll> ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T> a){ Uniq(a); unordered_map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
template<class T> map<T, ll> press_map(vector<T> a){ Uniq(a); map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const complex<T>& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline ll __lg(ull __n){ return sizeof(ull) * __CHAR_BIT__  - 1 - __builtin_clzll(__n); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }


#line 1 "utility/fast_io.cpp"



/**
 * @brief 高速入出力
 * @author えびちゃん
 * @see https://qiita.com/rsk0315_h4x/items/17a9cb12e0de5fd918f4
 */

#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <limits>
#include <string>
#include <type_traits>
#include <utility>

#line 1 "integer/bit.cpp"



/**
 * @brief ビット演算
 * @author えびちゃん
 */

// XXX integral promotion 関連の注意をあまりしていません

#include <climits>
#include <type_traits>

template <typename Tp>
constexpr auto countl_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
    if (n & mask) n >>= i;
    else res += i;
  }
  return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countl_zero(static_cast<value_type>(~n));
}

template <typename Tp>
constexpr auto countr_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1);
    if (!(n & mask)) res += i, n >>= i;
  }
  return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countr_zero(static_cast<value_type>(~n));
}

constexpr unsigned long long half_mask[] = {
  0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
  0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};

template <typename Tp>
constexpr auto popcount(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
    else n += n >> j;
  }
  return n & 0xFF;
}

template <typename Tp>
constexpr auto parity(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }


template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }

template <typename Tp>
int ilog2(Tp n) {
  return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }

template <typename Tp>
constexpr auto reverse(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
  }
  return n;
}


#line 20 "utility/fast_io.cpp"

namespace fast {
  static constexpr size_t buf_size = 1 << 17;
  static constexpr size_t margin = 1;
  static char inbuf[buf_size + margin] = {};
  static __attribute__((aligned(8))) char outbuf[buf_size + margin] = {};
  static __attribute__((aligned(8))) char minibuf[32];
  static constexpr size_t int_digits = 20;  // 18446744073709551615
  static constexpr uintmax_t digit_mask = 0x3030303030303030;
  static constexpr uintmax_t first_mask = 0x00FF00FF00FF00FF;
  static constexpr uintmax_t second_mask = 0x0000FFFF0000FFFF;
  static constexpr uintmax_t third_mask = 0x00000000FFFFFFFF;
  static constexpr uintmax_t tenpow[] = {
    1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
    1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000,
    100000000000000, 1000000000000000, 10000000000000000, 100000000000000000,
    1000000000000000000, 10000000000000000000u,
  };
  static __attribute__((aligned(8))) char inttab[40000] = {};  // 4-digit integers (10000 many)
  static char S_sep = ' ', S_end = '\n';
  template <typename Tp>
  using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;

  class scanner {
    char* pos = inbuf;
    char* endpos = inbuf + buf_size;

    void M_read_from_stdin() {
      endpos = inbuf + fread(pos, 1, buf_size, stdin);
    }
    void M_reread_from_stdin() {
      ptrdiff_t len = endpos - pos;
      if (!(inbuf + len <= pos)) return;
      memcpy(inbuf, pos, len);
      char* tmp = inbuf + len;
      endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
      *endpos = 0;
      pos = inbuf;
    }

  public:
    scanner() { M_read_from_stdin(); }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void scan_parallel(Integral& x) {
      if (__builtin_expect(endpos <= pos + int_digits, 0))
        M_reread_from_stdin();
      bool ends = false;
      typename std::make_unsigned<Integral>::type y = 0;
      bool neg = false;
      if (std::is_signed<Integral>::value && *pos == '-') {
        neg = true;
        ++pos;
      }
      do {
        memcpy(minibuf, pos, 8);
        intmax_t c = *(intmax_t*)minibuf;
        intmax_t d = (c & digit_mask) ^ digit_mask;
        int skip = 8;
        int shift = 8;
        if (d) {
          int ctz = countr_zero<uintmax_t>(d);
          if (ctz == 4) break;
          c &= (1L << (ctz-5)) - 1;
          int discarded = (68-ctz) / 8;
          shift -= discarded;
          c <<= discarded * 8;
          skip -= discarded;
          ends = true;
        }
        c |= digit_mask;
        c ^= digit_mask;
        c = ((c >> 8) + c*10) & first_mask;
        c = ((c >> 16) + c*100) & second_mask;
        c = ((c >> 32) + c*10000) & third_mask;
        y = y*tenpow[shift] + c;
        pos += skip;
      } while (!ends);
      x = (neg? -y: y);
      ++pos;
    }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void scan_serial(Integral& x) {
      if (__builtin_expect(endpos <= pos + int_digits, 0))
        M_reread_from_stdin();
      bool neg = false;
      if (std::is_signed<Integral>::value && *pos == '-') {
        neg = true;
        ++pos;
      }
      typename std::make_unsigned<Integral>::type y = *pos-'0';
      while (*++pos >= '0') y = 10*y + *pos-'0';
      x = (neg? -y: y);
      ++pos;
    }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    // Use scan_parallel(x) only when x may be too large (about 10^12).
    // Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
    void scan(Integral& x) { scan_serial(x); }

    void scan_serial(std::string& s) {
      // until first whitespace
      s = "";
      do {
        char* startpos = pos;
        while (*pos > ' ') ++pos;
        s += std::string(startpos, pos);
        if (*pos != 0) {
          ++pos;  // skip the space
          break;
        }
        M_reread_from_stdin();
      } while (true);
    }

    void scan(std::string& s) { scan_serial(s); }

    template <typename Tp, typename... Args>
    void scan(Tp& x, Args&&... xs) {
      scan(x);
      scan(std::forward<Args>(xs)...);
    }
  };

  class printer {
    char* pos = outbuf;

    void M_flush_stdout() {
      fwrite(outbuf, 1, pos-outbuf, stdout);
      pos = outbuf;
    }

    static int S_int_digits(uintmax_t n) {
      if (n < tenpow[16]) {  // 1
        if (n < tenpow[8]) {  // 2
          if (n < tenpow[4]) {  // 3
            if (n < tenpow[2]) {  // 4
              if (n < tenpow[1]) return 1;  // 5
              return 2;  // 5
            }
            if (n < tenpow[3]) return 3;  // 4
            return 4;  // 4
          }
          if (n < tenpow[6]) {  // 4
            if (n < tenpow[5]) return 5;  // 5
            return 6;  // 5
          }
          if (n < tenpow[7]) return 7;  // 5
          return 8;  // 5
        }
        if (n < tenpow[12]) {  // 3
          if (n < tenpow[10]) {  // 4
            if (n < tenpow[9]) return 9;  // 5
            return 10;  // 5
          }
          if (n < tenpow[11]) return 11;  // 5
          return 12;  // 5
        }
        if (n < tenpow[14]) {  // 4
          if (n < tenpow[13]) return 13;  // 5
          return 14;  // 5
        }
        if (n < tenpow[15]) return 15;  // 5
        return 16;  // 5
      }
      if (n < tenpow[18]) {  // 2
        if (n < tenpow[17]) return 17;  // 3
        return 18;  // 3
      }
      return 19;  // 2
      if (n < tenpow[19]) return 19;  // 3
      return 20;  // 3
    }

    void M_precompute() {
      uintmax_t const digit1 = 0x0200000002000000;
      uintmax_t const digit2 = 0xf600fffff6010000;
      uintmax_t const digit3 = 0xfff600fffff60100;
      uintmax_t const digit4 = 0xfffff600fffff601;
      uintmax_t counter = 0x3130303030303030;
      for (int i = 0, i4 = 0; i4 < 10; ++i4, counter += digit4)
        for (int i3 = 0; i3 < 10; ++i3, counter += digit3)
          for (int i2 = 0; i2 < 10; ++i2, counter += digit2)
            for (int i1 = 0; i1 < 5; ++i1, ++i, counter += digit1)
              *((uintmax_t*)inttab + i) = counter;
    }

  public:
    printer() { M_precompute(); }
    ~printer() { M_flush_stdout(); }

    void print(char c) {
      if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
      *pos++ = c;
    }

    template <size_t N>
    void print(char const(&s)[N]) {
      if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
      memcpy(pos, s, N-1);
      pos += N-1;
    }

    void print(char const* s) {
      // FIXME: strlen や memcpy などで定数倍高速化したい
      while (*s != 0) {
        *pos++ = *s++;
        if (pos == outbuf + buf_size) M_flush_stdout();
      }
    }

    void print(std::string const& s) { print(s.data()); }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void print(Integral x) {
      if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
        M_flush_stdout();
      if (x == 0) {
        *pos++ = '0';
        return;
      }
      if (x < 0) {
        *pos++ = '-';
        if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
          switch (sizeof x) {
          case 2: print("32768"); return;
          case 4: print("2147483648"); return;
          case 8: print("9223372036854775808"); return;
          }
        }
        x = -x;
      }

      typename std::make_unsigned<Integral>::type y = x;
      int len = S_int_digits(y);
      pos += len;
      char* tmp = pos;
      int w = (pos - outbuf) & 3;
      if (w > len) w = len;
      for (int i = w; i > 0; --i) {
        *--tmp = y % 10 + '0';
        y /= 10;
      }
      len -= w;
      while (len >= 4) {
        tmp -= 4;
        *(unsigned*)tmp = *((unsigned*)inttab + (y % 10000));
        len -= 4;
        if (len) y /= 10000;
      }
      while (len-- > 0) {
        *--tmp = y % 10 + '0';
        y /= 10;
      }
    }

    template <typename Tp, typename... Args>
    void print(Tp const& x, Args&&... xs) {
      if (sizeof...(Args) > 0) {
        print(x);
        print(S_sep);
        print(std::forward<Args>(xs)...);
      }
    }

    template <typename Tp>
    void println(Tp const& x) { print(x), print(S_end); }

    template <typename Tp, typename... Args>
    void println(Tp const& x, Args&&... xs) {
      print(x, std::forward<Args>(xs)...);
      print(S_end);
    }

    static void set_sep(char c) { S_sep = c; }
    static void set_end(char c) { S_end = c; }
  };
}  // fast::


template<class T> struct Eraseable_Heap{
    pq<T> q, e;
    Eraseable_Heap(uint n){
        vector<T> a(n + 1);
        a[n] = INF;
        q = pq<T>(greater<T>(), a);
    }
    void push(T a){ q.push(a); }
    T top() const { return q.top(); }
    void erase(T a){
        if(q.top() == a){
            q.pop();
            while(e.size() && q.top() == e.top()){
                q.pop();
                e.pop();
            }
        }
        else e.push(a);
    }
};
signed main(){
    fast::scanner cin;
    fast::printer cout;
    uint h,w;
    cin.scan(h,w);
    vector<pair<uint,uint>>a(w+1);
    for(uint i=0;i<w;i++)a[i]={i,i};
    a[w]={INF,INF};
    map<uint,uint>s(all(a));
    Eraseable_Heap<uint> q(w);
    for(uint i=0;i<h;i++){
        uint l,r;
        cin.scan(l,r);
        l--;
        auto p=s.lower_bound(l);
        int mx=-1;
        while(p->first<r){
            q.erase(p->first-p->second);
            mx=p->second;
            p=s.erase(p);
        }
        if(r!=w&&p->first!=r&&mx!=-1){
            s.insert(p,{r,mx});
            q.push(r-mx);
        }
        uint ans=q.top();
        if(ans==INF)cout.println("-1");
        else cout.println(ans+i+1);
    }
}


Measured memory_bytes: 15876