Problem: The only difference between easy and hard versions is constraints.

Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly T minutes.

In the player, Polycarp stores n songs, each of which is characterized by two parameters: t_i and g_i, where t_i is the length of the song in minutes (1 ≤ t_i ≤ 15), g_i is its genre (1 ≤ g_i ≤ 3).

Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the i-th song, he would spend exactly t_i minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.

Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly T, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.

Input

The first line of the input contains two integers n and T (1 ≤ n ≤ 15, 1 ≤ T ≤ 225) — the number of songs in the player and the required total duration, respectively.

Next, the n lines contain descriptions of songs: the i-th line contains two integers t_i and g_i (1 ≤ t_i ≤ 15, 1 ≤ g_i ≤ 3) — the duration of the i-th song and its genre, respectively.

Output

Output one integer — the number of different sequences of songs, the total length of exactly T, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo 10^9 + 7 (that is, the remainder when dividing the quantity by 10^9 + 7).

Examples

Input


3 3
1 1
1 2
1 3


Output


6


Input


3 3
1 1
1 1
1 3


Output


2


Input


4 10
5 3
2 1
3 2
5 1


Output


10

Note

In the first example, Polycarp can make any of the 6 possible playlist by rearranging the available songs: [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2] and [3, 2, 1] (indices of the songs are given).

In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of 2 possible ways: [1, 3, 2] and [2, 3, 1] (indices of the songs are given).

In the third example, Polycarp can make the following playlists: [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1], [1, 4], [4, 1], [2, 3, 4] and [4, 3, 2] (indices of the songs are given).

Solution (in JAVA):

Solution:
/*Author: Satyajeet Singh, Delhi Technological University*/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
 
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static boolean sieve[];
    static ArrayList<Integer> primes;
    static long factorial[],invFactorial[];
    static HashSet<Pair> graph[];
    static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
/****************************************Solutions Begins***************************************/
    static int n,T,input[],type[];
    static long dp[][];

    static long dfs(int mask,int t){

        if(dp[mask][t]!=-1){
            return dp[mask][t];
        }
        int s=0;
        for(int i=0;i<n;i++){
            if((mask&(1<<i))!=0){
                s+=input[i];
            }
        }
        if(s>T){
            return 0;
        }
        if(s==T){
            dp[mask][t]=1;
            return dp[mask][t];
        }
        long ans=0;
        for(int i=0;i<n;i++){
            if((mask&(1<<i))==0&&type[i]!=t){
                ans=(ans+dfs(mask|(1<<i),type[i]))%mod;
            }
        }
        dp[mask][t]=ans;
        return dp[mask][t];
    }
    public static void main (String[] args) throws Exception {
        String st[]=nl();
        n=pi(st[0]);
        T=pi(st[1]);
        input=new int[n];
        type=new int[n];
        for(int i=0;i<n;i++){
            st=nl();
            input[i]=pi(st[0]);
            type[i]=pi(st[1]);
        }
        dp=new long[1<<n][4];
        for(long arr[]:dp)
            Arrays.fill(arr,-1);
        long ans=dfs(0,0);
       // debug(dp);

        out.println(ans);
/****************************************Solutions Ends**************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins************************************************/
    static String[] nl() throws Exception{
        return br.readLine().split(" ");
    }
    static String[] nls() throws Exception{
        return br.readLine().split("");
    }
    static int pi(String str) {
        return Integer.parseInt(str);
    }
    static long pl(String str){
        return Long.parseLong(str);
    }
    static double pd(String str){
        return Double.parseDouble(str);
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.00000000000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static void printMask(long mask){
        System.out.println(Long.toBinaryString(mask));
    }
    static int countBit(int mask){
        int ans=0;
        while(mask!=0){
            if(mask%2==1){
                ans++;
            }
            mask/=2;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new HashSet[n];
        for(int i=0;i<n;i++){
            graph[i]=new HashSet<>();
        }
    }
    static void addEdge(int a,int b){
        graph[a].add(new Pair(b,1));
    }
    static void addEdge(int a,int b,int c){
        graph[a].add(new Pair(b,c));
    }    
/*********************************************PAIR********************************************************/
    static class PairComp implements Comparator<Pair>{
        public int compare(Pair p1,Pair p2){
            return ((p1.u+p1.v)-(p2.u+p2.v));
        }
    }
    static class Pair implements Comparable<Pair> {
        int u;
        int v;
        int index=-1;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public int compareTo(Pair other) {
            if(index!=other.index)
                return Long.compare(index, other.index);
            return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*************************************************/
    static class PairCompL implements Comparator<Pairl>{
        public int compare(Pairl p1,Pairl p2){
            if((p1.u+2*p1.v)-(p2.u+2*p2.v)<0){
                return -1;
            }
            else if((p1.u+2*p1.v)-(p2.u+2*p2.v)>0){
                return 1;
            }
            else{
                return 0;
            }
        }
    }
    static class Pairl implements Comparable<Pairl> {
            long u;
            long v;
            int index=-1;
            public Pairl(long u, long v) {
                this.u = u;
                this.v = v;
            }
    
            public int hashCode() {
                int hu = (int) (u ^ (u >>> 32));
                int hv = (int) (v ^ (v >>> 32));
                return 31 * hu + hv;
            }
    
            public boolean equals(Object o) {
                Pair other = (Pair) o;
                return u == other.u && v == other.v;
            }
    
            public int compareTo(Pairl other) {
                if(index!=other.index)
                    return Long.compare(index, other.index);
                return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
            }
    
            public String toString() {
                return "[u=" + u + ", v=" + v + "]";
            }
        }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o) {
        if(!oj)
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c) {
        long x=1;
        long y=a;
        while(b > 0){
            if(b%2 == 1){
                x=(x*y)%c;
            }
            y = (y*y)%c; // squaring the base
            b /= 2;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y)
    {
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; // a is greater number
        b = (x < y) ? x : y; // b is smaller number
        r = b;
        while(a % b != 0)
        {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
/******************************************SIEVE**********************************************************/
    static void sieveMake(int n){
        sieve=new boolean[n];
        Arrays.fill(sieve,true);
        sieve[0]=false;
        sieve[1]=false;
        for(int i=2;i*i<n;i++){
            if(sieve[i]){
                for(int j=i*i;j<n;j+=i){
                    sieve[j]=false;
                }
            }
        }
        primes=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            if(sieve[i]){
                primes.add(i);
            }
        }        
    }
/********************************************End***********************************************************/
}