codeforces 451 E Devu and Flowers
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import java.math.BigDecimal;import java.math.BigInteger;import java.util.Scanner;import java.util.Vector;public class Main {static final long mod=1000000007;public static void main(String[] args) {long a[]=new long[20];Scanner sc=new Scanner(System.in);int n=sc.nextInt();long s=sc.nextLong();for(int i=0;i<n;i++)a[i]=sc.nextLong();int len=(1<<n);long ans=0;for(int i=0;i<len;i++){long x=s;int flag=1;for(int j=0;j<n;j++)if(((i>>j)&1)==1){flag*=-1;x-=a[j]+1;}if(x<0)continue;ans=(ans+flag*lucas(x+n-1,n-1))%mod;ans=(ans+mod)%mod;}System.out.println(ans);}static long lucas(long a,long b){if(b==0)return 1;return getc(a%mod,b%mod)*lucas(a/mod,b/mod)%mod;}static long getc(long a,long b){if(a<b)return 0;long ans=1;for(long i=a-b+1;i<=a;i++)ans=ans*i%mod;long t=1;for(long i=1;i<=b;i++)t=t*i%mod;return ans*qpow(t,mod-2)%mod;}static long qpow(long a,long b){long ans=1;while(b!=0){if((b&1)==1){ans=a*ans%mod;}a=a*a%mod;b>>=1;}return ans;}}
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