#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>

//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>

using namespace std;

#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)

#define ECH(it, A) for (typeof((A).begin()) it=(A).begin(); it != (A).end(); ++it)
#define rECH(it, A) for (__typeof((A).rbegin()) it=(A).rbegin(); it != (A).rend(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (upper_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()

#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) {                      \
REP(i, n){                                    \
REP(j, m-1) cout << A[i][j] << " ";     \
cout << A[i][m-1] << endl;                \
}                                            \
}
#define Display_1(A, n, m) {                    \
REP_1(i, n){                                \
REP_1(j, m-1) cout << A[i][j] << " ";   \
cout << A[i][m] << endl;                \
}                                            \
}

typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;

template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}

template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}

template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline T0& RDD(T0&a, T1&b){RDD(a),RDD(b); return a;}
template<class T0,class T1,class T2>inline T1& RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c); return a;}

template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}

template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T> inline void CLR(queue<T> &Q){while (!Q.empty()) Q.pop();}

template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}

template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}


//}

/** Constant List .. **/ //{

const int MOD = 998244353;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;

const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};

//}

/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{

template<class T> inline bool checkMin(T &a,const T b){return b < a ? a = b, 1 : 0;}
template<class T> inline bool checkMax(T &a,const T b){return a < b ? a = b, 1 : 0;}
template <class T, class C> inline bool checkUpd(T& a, const T b, C c){return c(b,a) ? a = b, 1 : 0;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}

inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};

//}



// <<= '2. Number Theory .,//{
namespace NT{
//#define gcd __gcd
    int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
//    inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
    
    inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
    inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
    
    /* Ä£ÊýÁ½±¶¸ÕºÃ³¬ int Ê±¡£
     inline int sum(uint a, int b){a += b; a %= MOD;if (a < 0) a += MOD; return a;}
     inline void INC(int &a, int b){a = sum(a, b);}
     */
    
    inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
    inline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}
    inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
    //inline int pdt(int a, int b){return (LL)a * b % MOD;}
    inline int pdt(int x,int y) {
        int ret; __asm__ __volatile__ ("\tmull %%ebx\n\tdivl %%ecx\n":"=d"(ret):"a"(x),"b"(y),"c"(MOD));
        return ret;
    }
    
    
    inline int gcd(int m, int n, int &x, int &y){
        
        x = 1, y = 0; int xx = 0, yy = 1, q;
        
        while (1){
            q = m / n, m %= n;
            if (!m){x = xx, y = yy; return n;}
            DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
            q = n / m, n %= m;
            if (!n) return m;
            DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
        }
    }
    
    inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
    inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
    inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
    inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
    
    inline int pow(int a, LL b){
        int c(1); while (b){
            if (b&1) MUL(c, a);
            MUL(a, a), b >>= 1;
        }
        return c;
    }
    
    template<class T> inline T pow(T a, LL b){
        T c(1); while (b){
            if (b&1) c *= a;
            a *= a, b >>= 1;
        }
        return c;
    }
    
    template<class T> inline T pow(T a, int b){
        return pow(a, (LL)b);
    }
    
    inline int _I(int b){
        int a = MOD, x1 = 0, x2 = 1, q; while (1){
            q = a / b, a %= b;
            if (!a) return x2;
            DEC(x1, pdt(q, x2));
            
            q = b / a, b %= a;
            if (!b) return x1;
            DEC(x2, pdt(q, x1));
        }
    }
    
    inline void DIV(int &a, int b){MUL(a, _I(b));}
    inline int qtt(int a, int b){return pdt(a, _I(b));}
    
    struct Int{
        int val;
        
        operator int() const{return val;}
        
        Int(int _val = 0):val(_val){
            val %= MOD; if (val < 0) val += MOD;
        }
        Int(LL _val):val(_val){
            _val %= MOD; if (_val < 0) _val += MOD;
            val = _val;
        }
        
        Int& operator +=(const int& rhs){INC(val, rhs);rTs;}
        Int operator +(const int& rhs) const{return sum(val, rhs);}
        Int& operator -=(const int& rhs){DEC(val, rhs);rTs;}
        Int operator -(const int& rhs) const{return dff(val, rhs);}
        Int& operator *=(const int& rhs){MUL(val, rhs);rTs;}
        Int operator *(const int& rhs) const{return pdt(val, rhs);}
        Int& operator /=(const int& rhs){DIV(val, rhs);rTs;}
        Int operator /(const int& rhs) const{return qtt(val, rhs);}
        Int operator-()const{return MOD-*this;}
    };
    
} using namespace NT;//}

// <<= 'Bignum ., //{
namespace BIGNUM{
    
    const int __base = 1e8;
    const int P10[] = {1, 10, int(1e2), int(1e3), int(1e4), int(1e5), int(1e6), int(1e7), int(1e8), int(1e9)};
    const int MAX_BUF_SIZE = 109;
    char __buf[MAX_BUF_SIZE];
    
    class bignum{
        friend istream& operator>>(istream&, bignum&);
        friend ostream& operator<<(ostream&, const bignum&);
        friend bignum operator +(const bignum&, const bignum&);
        friend bignum operator -(const bignum&, const bignum&);
        friend bignum operator *(const bignum&, const bignum&);
        friend bignum operator /(const bignum&, const bignum&);
        friend bignum operator %(const bignum&, const bignum&);
        friend bignum operator +(const bignum&, const int&);
        friend bignum operator -(const bignum&, const int&);
        friend bignum operator *(const bignum&, const int&);
        friend bignum operator /(const bignum&, const int&);
        friend bignum operator %(const bignum&, const int&);
        friend bool operator ==(const bignum&, const bignum&);
        friend bool operator !=(const bignum&, const bignum&);
        friend bool operator <(const bignum&, const bignum&);
        friend bool operator >(const bignum&, const bignum&);
        friend bool operator <=(const bignum&, const bignum&);
        friend bool operator >=(const bignum&, const bignum&);
        friend bool operator ==(const bignum&, const int&);
        friend bool operator !=(const bignum&, const int&);
        friend bool operator <(const bignum&, const int&);
        friend bool operator >(const bignum&, const int&);
        friend bool operator <=(const bignum&, const int&);
        friend bool operator >=(const bignum&, const int&);
        friend int do_comp(const bignum&, const int&);
        friend int do_comp(const bignum&, const bignum&);
        friend void divide(const bignum&, const bignum&, bignum&, bignum&);
        friend bignum pow(bignum, int);
        friend bignum pow(int, int);
    public:
        inline bignum(){};
        inline bignum(int s){
            while (s) data.PB(s%__base), s/=__base;
            if (data.empty()) data.PB(0);
        }
        
        inline bignum(long long s){
            while (s) data.PB(int(s%__base)), s/=__base;
            if (data.empty()) data.PB(0);
        }
        
        inline bignum(string s){
            int t, i; CLR(data);
            for (i=int(s.size())-8;i>0;i-=8){
                istringstream(s.substr(i, 8)) >> t;
                data.PB(t);
            }
            istringstream(s.substr(0, i+8)) >> t;
            data.PB(t);
        }
        
        void input(){
            CLR(data); RS(__buf); int t = 0, c = 0;
            DWN(i, strlen(__buf), 0){
                t += P10[c] * (int(__buf[i]) - '0'), ++c;
                if (c == 8) data.PB(t), c = t = 0;
            }
            if (c) data.PB(t);
        }
        
        bignum&operator=(int);
        bignum&operator=(const string&);
        bignum&operator=(const bignum&);
        bignum&operator +=(const bignum&);
        bignum&operator -=(const bignum&);
        bignum&operator *=(const bignum&);
        bignum&operator /=(const bignum&);
        bignum&operator %=(const bignum&);
        bignum&operator +=(const int&);
        bignum&operator -=(const int&);
        bignum&operator *=(const int&);
        bignum&operator /=(const int&);
        bignum&operator %=(const int&);
        bool undefined();
        int do_try(const int&);
        int do_try(const bignum&);
        void do_trim();
        list<int> data;
        
        int size(){
            list<int>::iterator it; int res = 0;
            for (it=data.begin(); it!=data.end();it++)
                res += 8;
            it--;
            if (*it >= 10000) {
                if ( (*it) >= 1000000) {if (*it >=10000000) ; else res--;}
                else {if ((*it) >= 100000) res-=2; else res-=3;}
            }
            else
                if ( (*it) >= 100) {if (*it >=1000) res-=4; else res-=5;}
                else {if ((*it) >= 10) res-=6; else res-=7;}
            
            return res;
        }
        
        void do_reserve(int a){
            if (a <= 0) return;
            list<int>::iterator it;
            for (it=data.begin(); it!=data.end() && a>0; it++) a-=8;
            if (it == data.end() && a>=0) return;
            a+=8, it--; int f = 1;
            for (int i=0;i<a;i++) f *= 10; (*it) %= f;
            data.erase(++it, data.end());
            do_trim();
        }
    };
    
    inline bignum&bignum::operator =(const bignum&a){
        data.clear();
        for (list<int>::const_iterator i=a.data.begin();i!=a.data.end();i++){
            data.PB(*i);
        }
        return*this;
    }
    inline bignum&bignum::operator =(const string&a){
        return*this=bignum(a);
    }
    inline bignum&bignum::operator =(int a){
        return*this=bignum(a);
    }
    
    inline istream& operator>>(istream& input, bignum& a){
        string s; int t, i; input >> s; a.data.clear();
        for (i=int(s.size())-8;i>0;i-=8){
            istringstream(s.substr(i, 8)) >> t;
            a.data.PB(t);
        }
        istringstream(s.substr(0, i+8)) >> t;
        a.data.PB(t);
        return input;
    }
    
    inline ostream& operator<<(ostream& output, const bignum& a){
        list<int>::const_reverse_iterator i=a.data.rbegin();
        output << *i;
        for (i++;i!=a.data.rend();i++){
            if (*i >= 10000) {
                if (*i >= 1000000) {if (*i>=10000000) cout << *i; else cout << 0 << *i;}
                else {if (*i>=100000) cout << "00" << *i; else cout << "000" << *i;}
            }
            else {
                if (*i >= 100) {if (*i>=1000)  cout << "0000" << *i; else cout << "00000" << *i;}
                else { if (*i>=10) cout << "000000" << *i; else cout << "0000000" << *i;}
            }
        }
        return output;
    }
    
    inline bool bignum::undefined(){
        return data.empty();
    }
    
    inline int do_comp(const bignum& a, const bignum& b){
        if (a.data.size()<b.data.size()) return -1; if (a.data.size()>b.data.size()) return 1;
        list<int>::const_reverse_iterator i; list<int>::const_reverse_iterator j;
        for (i=a.data.rbegin(),j=b.data.rbegin(); j!=b.data.rend(); i++,j++){
            if (*i<*j) return -1;              //!!!!
            if (*i>*j) return 1;
        }
        return 0;
    }
    inline int do_comp(const bignum& a, const int& b){
        return do_comp(a, bignum(b));
    }
    
    inline bool operator ==(const bignum& a, const bignum& b){
        return do_comp(a, b) == 0;
    }
    inline bool operator !=(const bignum& a, const bignum& b){
        return do_comp(a, b) != 0;
    }
    inline bool operator <(const bignum& a, const bignum& b){
        return do_comp(a, b) == -1;
    }
    inline bool operator >(const bignum& a, const bignum& b){
        return do_comp(a, b) == 1;
    }
    inline bool operator <=(const bignum& a, const bignum& b){
        return do_comp(a, b) != 1;
    }
    inline bool operator >=(const bignum& a, const bignum& b){
        return do_comp(a, b) != -1;
    }
    
    inline bool operator ==(const bignum& a, const int& b){
        return do_comp(a, b) == 0;
    }
    inline bool operator !=(const bignum& a, const int& b){
        return do_comp(a, b) != 0;
    }
    inline bool operator <(const bignum& a, const int& b){
        return do_comp(a, b) == -1;
    }
    inline bool operator >(const bignum& a, const int& b){
        return do_comp(a, b) == 1;
    }
    inline bool operator <=(const bignum& a, const int& b){
        return do_comp(a, b) != 1;
    }
    inline bool operator >=(const bignum& a, const int& b){
        return do_comp(a, b) != -1;
    }
    
    inline void bignum::do_trim(){
        while (data.size()>1&&data.back()==0) data.pop_back();
    }
    
    inline bignum& bignum::operator +=(const bignum& a){
        list<int>::iterator i; list<int>::const_iterator j; int t = 0;
        for (i=data.begin(),j=a.data.begin(); i!=data.end()&&j!=a.data.end(); i++,j++){
            *i+=*j+t; t=*i/__base; *i%=__base;
        }
        while (i!=data.end()) {*i+=t; t=*i/__base; *i%=__base; i++;}
        while (j!=a.data.end()) {data.PB(t+*j); t=data.back()/__base; data.back()%=__base; j++;}
        if (t!=0) data.PB(t);
        return *this;
    }
    
    inline bignum& bignum::operator -=(const bignum& a){
        list<int>::iterator i; list<int>::const_iterator j; int t = 0;
        for (i=data.begin(),j=a.data.begin(); j!=a.data.end(); i++,j++){
            *i -= t+*j; if (*i>=0) t=0; else *i+=__base, t=1;
        }
        while (i!=data.end()) {*i-=t; if (*i>=0) t=0;else *i+=__base, t=1; i++;}
        (*this).do_trim();
        return *this;
    }
    
    inline bignum& bignum::operator +=(const int& a){
        return (*this)+=bignum(a);
    }
    
    inline bignum& bignum::operator -=(const int& a){
        return (*this)-=bignum(a);
    }
    
    inline bignum operator +(const bignum& a, const bignum& b){
        list<int>::const_iterator i, j; bignum c; int t = 0;
        for (i=a.data.begin(),j=b.data.begin(); i!=a.data.end()&&j!=b.data.end(); i++,j++){
            c.data.PB(t+*i+*j);
            t=c.data.back()/__base; c.data.back()%=__base;
        }
        while (i!=a.data.end()) {c.data.PB(t+*i); t=c.data.back()/__base; c.data.back()%=__base; i++;}
        while (j!=b.data.end()) {c.data.PB(t+*j); t=c.data.back()/__base; c.data.back()%=__base; j++;}
        if (t!=0) c.data.PB(t);
        return c;
    }
    
    inline bignum operator -(const bignum& a, const bignum& b){
        list<int>::const_iterator i, j; bignum c; int t = 0;
        for (i=a.data.begin(),j=b.data.begin(); j!=b.data.end(); i++,j++){
            t = *i - t;
            if (t>=*j) c.data.PB(t-*j), t=0;
            else c.data.PB(t+__base-*j), t=1;
        }
        while (i!=a.data.end()) {t=*i-t; if (t>=0) c.data.PB(t), t=0;else c.data.PB(t+__base), t=1; i++;}
        c.do_trim();
        return c;
    }
    
    inline bignum operator *(const bignum& a, const bignum& b){
        list<int>::const_iterator i, j; list<int>::iterator k, kk; bignum c; long long t = 0;
        
        for (int i=0;i<a.data.size()+b.data.size();i++) c.data.PB(0);
        for (i=a.data.begin(),k=c.data.begin(); i!=a.data.end(); i++,k++){
            for (j=b.data.begin(),kk=k; j!=b.data.end(); j++,kk++){
                t+=(long long)(*i)*(*j)+(*kk);
                *kk=int(t%__base); t/=__base;
            }
            *kk+=t; t=0;
        }
        c.do_trim();
        return c;
    }
    
    inline int bignum::do_try(const bignum& a){
        int l = 1, r = 99999999, m, t;
        while (l+2<r){
            m = (l + r) / 2;
            t = do_comp(*this, a*bignum(m));
            if (t==0) return m;
            if (t<0) r = m - 1;
            else l = m;
        }
        while (do_comp(*this, a*bignum(r))<0) r--;
        return r;
    }
    
    inline void divide(const bignum& a, const bignum& b, bignum& d, bignum& r){
        list<int>::const_reverse_iterator i = a.data.rbegin(); int t;
        d = bignum(0); r = bignum(0);
        do {
            while (r<b&&i!=a.data.rend()){d.data.push_front(0);r.data.push_front(*i);r.do_trim();i++;}
            if (r>=b){
                t = r.do_try(b); d.data.front() = t;
                r-=(b*bignum(t));
            }
        } while (i!=a.data.rend());
        d.do_trim();
    }
    
    inline bignum operator /(const bignum& a, const bignum& b){
        bignum d, r;
        divide(a, b, d, r);
        return d;
    }
    
    inline bignum operator %(const bignum& a, const bignum& b){
        bignum d, r;
        divide(a, b, d, r);
        return r;
    }
    
    inline bignum operator +(const bignum& a, const int& b){
        return a+bignum(b);
    }
    
    inline bignum operator -(const bignum& a, const int& b){
        return a-bignum(b);
    }
    
    inline bignum operator *(const bignum& a, const int& b){
        return a*bignum(b);
    }
    
    inline bignum operator /(const bignum& a, const int& b){
        return a/bignum(b);
    }
    
    inline bignum operator %(const bignum& a, const int& b){
        return a%bignum(b);
    }
    
    inline bignum& bignum::operator *=(const bignum& a){
        (*this) = (*this) * a;
        return *this;
    }
    
    inline bignum& bignum::operator /=(const bignum& a){
        (*this) = (*this) / a;
        return *this;
    }
    
    inline bignum& bignum::operator %=(const bignum& a){
        (*this) = (*this) % a;
        return *this;
    }
    
    inline bignum& bignum::operator *=(const int& a){
        return (*this)*=bignum(a);
    }
    
    inline bignum& bignum::operator /=(const int& a){
        return (*this)/=bignum(a);
    }
    
    inline bignum& bignum::operator %=(const int& a){
        return (*this)%=bignum(a);
    }
    
    inline bignum pow(bignum a,int b){
        bignum c(1);
        while (b!=0) {
            if (b&1) c *= a;
            a = a * a; b >>= 1;
        }
        return c;
    }
    inline bignum pow(int a, int b){
        return pow(bignum(a), b);
    }
    
} using namespace BIGNUM;
//}

/** Bitwise Operation **/

inline int count_bits(int x){
    x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
    x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
    x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
    x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
    x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
    return x;
}

inline int count_bits_32(int x){
    x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
    x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
    x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
    x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
    x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
    return x;
}

inline int count_bits_16(int x){
    x = (x & 0x00005555) + ((x & 0x0000aaaa) >> 1);
    x = (x & 0x00003333) + ((x & 0x0000cccc) >> 2);
    x = (x & 0x00000f0f) + ((x & 0x0000f0f0) >> 4);
    x = (x & 0x000000ff) + ((x & 0x0000ff00) >> 8);
    return x;
}

inline int count_bits_8(int x){
    x = (x & 0x00000055) + ((x & 0x000000aa) >> 1);
    x = (x & 0x00000033) + ((x & 0x000000cc) >> 2);
    x = (x & 0x0000000f) + ((x & 0x0000f0f0) >> 4);
    return x;
}

int reverse_bits(int x){
    x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
    x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
    x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
    x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
    x = ((x >> 16) & 0x0000ffff) | ((x << 16) & 0xffff0000);
    return x;
}
template<class T> inline T low_bit(T x) {return x & -x;}

template<class T> inline T high_bit(T x) {
    T p = low_bit(x);
    while (p != x) x -= p, p = low_bit(x);
    return p;
}

//}



/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
    char c;while(!d);x=c-'0';while(d)p;
    return x;
}
template<class T> inline T& RDD(T &x){
    char c;while(g,c!='-'&&!isdigit(c));
    if (c=='-'){x='0'-g;while(d)n;}
    else{x=c-'0';while(d)p;}
    return x;
}
inline DB& RF(DB &x){
    //scanf("%lf", &x);
    char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
    if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
    else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
    else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
    else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
    return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
    //gets(s);
    scanf("%s", s);
    return s;
}

LL last_ans; int Case; template<class T> inline void OT(const T &x){
    //printf("Case #%d: ", ++Case);
    //printf("%lld\n", x);
    printf("%.9f\n", x);
    //printf("%d\n", x);
    //cout << x << endl;
    //last_ans = x;
}


//}/* .................................................................................................................................. */
#include <iostream>
using namespace std;

const int N = int(1e6) + 9;
LL a[N], b[N];
int n;

bool ok() {
    REP(i, n) if (a[i] != b[i]) return 0;
    return 1;
}

int main() {
    
    int n, k;
    RD(n, k);
    n = (n+1)/2;
    puts(n >= k ? "YES" : "NO");
  
}


// a0 a1 a2 a3 a4 a5
// a[l] + a[r] - a[x]






Measured memory_bytes: 256