Once upon a time, Oolimry saw a suffix array. He wondered how many strings can produce this suffix array. 

More formally, given a suffix array of length n and having an alphabet size k, count the number of strings that produce such a suffix array. 

Let s be a string of length n. Then the i-th suffix of s is the substring s[i … n-1]. A suffix array is the array of integers that represent the starting indexes of all the suffixes of a given string, after the suffixes are sorted in the lexicographic order. For example, the suffix array of oolimry is [3,2,4,1,0,5,6] as the array of sorted suffixes is [imry,limry,mry,olimry,oolimry,ry,y]. 

A string x is lexicographically smaller than string y, if either x is a prefix of y (and x≠ y), or there exists such i that x_i < y_i, and for any 1≤ j < i , x_j = y_j.

Input

The first line contain 2 integers n and k (1 ≤ n ≤ 200000,1 ≤ k ≤ 200000) — the length of the suffix array and the alphabet size respectively.

The second line contains n integers s_0, s_1, s_2, …, s_{n-1} (0 ≤ s_i ≤ n-1) where s_i is the i-th element of the suffix array i.e. the starting position of the i-th lexicographically smallest suffix. It is guaranteed that for all 0 ≤ i< j ≤ n-1, s_i ≠ s_j.

Output

Print how many strings produce such a suffix array. Since the number can be very large, print the answer modulo 998244353.

Examples

Input


3 2
0 2 1


Output


1

Input


5 1
0 1 2 3 4


Output


0

Input


6 200000
0 1 2 3 4 5


Output


822243495

Input


7 6
3 2 4 1 0 5 6


Output


36

Note

In the first test case, "abb" is the only possible solution. 

In the second test case, it can be easily shown no possible strings exist as all the letters have to be equal. 

In the fourth test case, one possible string is "ddbacef".

Please remember to print your answers modulo 998244353.
/*{{{*/
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include<bitset>
#include<vector>
#include<limits.h>
#include<assert.h>
#define SZ(X) ((int)(X).size())
#define ALL(X) (X).begin(), (X).end()
#define REP(I, N) for (int I = 0; I < (N); ++I)
#define REPP(I, A, B) for (int I = (A); I < (B); ++I)
#define FOR(I, A, B) for (int I = (A); I <= (B); ++I)
#define FORS(I, S) for (int I = 0; S[I]; ++I)
#define RS(X) scanf("%s", (X))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)
#define MP make_pair
#define PB emplace_back
#define MS0(X) memset((X), 0, sizeof((X)))
#define MS1(X) memset((X), -1, sizeof((X)))
#define LEN(X) strlen(X)
#define F first
#define S second
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<LL> VL;
typedef vector<PII> VPII;
typedef pair<LL,LL> PLL;
typedef vector<PLL> VPLL;
template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }
template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T,class U> void _W(const pair<T,U> &x) {_W(x.F); putchar(' '); _W(x.S);}
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }
#ifdef HOME
 #define DEBUG(...) {printf("[DEBUG] ");W(__VA_ARGS__);}
#else
 #define DEBUG(...)
#endif
int MOD = 1e9+7;
void ADD(LL& x,LL v){x=(x+v)%MOD;if(x<0)x+=MOD;}
/*}}}*/
const int SIZE = 1<<20;
const int COMBINATION_SIZE = 1<<21;
long long mypow(long long x, long long y, long long mod = MOD){
    long long res=1;
    while(y){
        if(y&1) {
            res = res * x % mod;
        }
        y >>= 1;
        x = x * x % mod;
    }
    return res;
}
struct Combination {
    long long fac[COMBINATION_SIZE], inv[COMBINATION_SIZE];
    bool built = 0;
    void build(){
        assert(MOD >= COMBINATION_SIZE);
        fac[0] = 1;
        for(int i = 1; i < COMBINATION_SIZE; i++) {
            fac[i] = fac[i - 1] * i % MOD;
        }
        inv[COMBINATION_SIZE - 1] = mypow(fac[COMBINATION_SIZE - 1], MOD - 2);
        for(int i = COMBINATION_SIZE - 2; i >= 0; i--) {
            inv[i] = inv[i + 1] * (i + 1) % MOD;
        }
    }
    long long C(int x, int y){
        if(y < 0 || y > x) {
            return 0;
        }
        if(!built) {
            built = 1;
            build();
        }
        return fac[x] * inv[y] % MOD * inv[x-y] % MOD;
    }
} comb;
/*
int main() {
    int n;
    scanf("%d", &n);
    for(int i = 0; i < n; i++) {
        int a, b;
        scanf("%d%d", &a, &b);
        printf("%lld\n", comb.C(a, b));
    }
    return 0;
}
*/
int s[SIZE],pos[SIZE];
int n,k;
void solve() {
    s[0]=n;
    pos[n]=0;
    int gap=0;
    REPP(i,1,n){
        if(pos[s[i]+1]>pos[s[i+1]+1]){
            gap++;
        }
    }
    if(gap>=k){
        W(0);
    }else{
        W(comb.C(n+k-1-gap,n));
    }
}
void input() {
    R(n,k);
    FOR(i,1,n){
        R(s[i]);
        pos[s[i]]=i;
    }
}
int main(){
    MOD=998244353;
    input();
    solve();
    return 0;
}
